Can the Inverse Trigonometric functions be calculated without Look-Up Tables?
EDIT:A computer calculates it by closing in on the value of the angle after iterating (+/-pi)/(Some constant). A user posted a link to the CORDIC method wiki but I can't understand it still after a day.
I tested the series expansion with a bunch of angles and close in on the angle after very iterations of the series:
Here I used Excel's Trig functions to find Sin, cos, tan, csc, sec, & tan for ".6" Radians. Using the Y=sin(y), & X=cos(x), & m=tan(y/x) I close in on the value of ARCTAN(Y/X) quickly and reliably.
Original Question:
I was thinking of this problem:
Given a Unit Circle and a line from the origin through it's circumference at some point where the X value is known but not the Y value find the Y-value.
You can use the pythagorean theorem to find Y or you can use ARCCOS(x) to get the angle "A" and then solve sin(A) to get the Y-value.
So I was in Excel and the Inverse Trig functions aren't available functions in MS Excel. So I made a "Look-Up-Table" of the Cosine of Angles 0-90 down to the third decimal point.
This made me wonder if it was possible to calculate ARCSIN, ARCCOS, or ARCTAN using mathematical formulas and logic. I then figured MS Excel didn't have them as functions because that would require huge LUTs to be loaded into the memory every time Excel is opened as being accurate to the 3rd decimal takes tens of thousands of cells. So I figured they just don't allow those functions.
I then read on wikipedia that they can be derived but it didn't explain. Does anyone know if the inverse trig functons can be derived with a mathematical proof or are they simply "arcsin(y)=the angle that a ray from the origin must be in order for it to cross the Circumference of a circle at a right angle at a point with a y-value of "y""?
This seems electronic enough because waveforms, frequency, phase angle and Angular velocity come into play a lot with complex impedance.
calculus
asked Dec 2 at 20:34
Danny Sebahar
11
migrated from electronics.stackexchange.com Dec 9 at 4:00
This question came from our site for electronics and electrical engineering professionals, students, and enthusiasts.
|
show 2 more comments
EDIT:A computer calculates it by closing in on the value of the angle after iterating (+/-pi)/(Some constant). A user posted a link to the CORDIC method wiki but I can't understand it still after a day.
I tested the series expansion with a bunch of angles and close in on the angle after very iterations of the series:
Here I used Excel's Trig functions to find Sin, cos, tan, csc, sec, & tan for ".6" Radians. Using the Y=sin(y), & X=cos(x), & m=tan(y/x) I close in on the value of ARCTAN(Y/X) quickly and reliably.
Original Question:
I was thinking of this problem:
Given a Unit Circle and a line from the origin through it's circumference at some point where the X value is known but not the Y value find the Y-value.
You can use the pythagorean theorem to find Y or you can use ARCCOS(x) to get the angle "A" and then solve sin(A) to get the Y-value.
So I was in Excel and the Inverse Trig functions aren't available functions in MS Excel. So I made a "Look-Up-Table" of the Cosine of Angles 0-90 down to the third decimal point.
This made me wonder if it was possible to calculate ARCSIN, ARCCOS, or ARCTAN using mathematical formulas and logic. I then figured MS Excel didn't have them as functions because that would require huge LUTs to be loaded into the memory every time Excel is opened as being accurate to the 3rd decimal takes tens of thousands of cells. So I figured they just don't allow those functions.
I then read on wikipedia that they can be derived but it didn't explain. Does anyone know if the inverse trig functons can be derived with a mathematical proof or are they simply "arcsin(y)=the angle that a ray from the origin must be in order for it to cross the Circumference of a circle at a right angle at a point with a y-value of "y""?
This seems electronic enough because waveforms, frequency, phase angle and Angular velocity come into play a lot with complex impedance.
calculus
asked Dec 2 at 20:34
Danny Sebahar
11
migrated from electronics.stackexchange.com Dec 9 at 4:00
This question came from our site for electronics and electrical engineering professionals, students, and enthusiasts.
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
1
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22
|
show 2 more comments
EDIT:A computer calculates it by closing in on the value of the angle after iterating (+/-pi)/(Some constant). A user posted a link to the CORDIC method wiki but I can't understand it still after a day.
I tested the series expansion with a bunch of angles and close in on the angle after very iterations of the series:
Here I used Excel's Trig functions to find Sin, cos, tan, csc, sec, & tan for ".6" Radians. Using the Y=sin(y), & X=cos(x), & m=tan(y/x) I close in on the value of ARCTAN(Y/X) quickly and reliably.
Original Question:
I was thinking of this problem:
Given a Unit Circle and a line from the origin through it's circumference at some point where the X value is known but not the Y value find the Y-value.
You can use the pythagorean theorem to find Y or you can use ARCCOS(x) to get the angle "A" and then solve sin(A) to get the Y-value.
So I was in Excel and the Inverse Trig functions aren't available functions in MS Excel. So I made a "Look-Up-Table" of the Cosine of Angles 0-90 down to the third decimal point.
This made me wonder if it was possible to calculate ARCSIN, ARCCOS, or ARCTAN using mathematical formulas and logic. I then figured MS Excel didn't have them as functions because that would require huge LUTs to be loaded into the memory every time Excel is opened as being accurate to the 3rd decimal takes tens of thousands of cells. So I figured they just don't allow those functions.
I then read on wikipedia that they can be derived but it didn't explain. Does anyone know if the inverse trig functons can be derived with a mathematical proof or are they simply "arcsin(y)=the angle that a ray from the origin must be in order for it to cross the Circumference of a circle at a right angle at a point with a y-value of "y""?
This seems electronic enough because waveforms, frequency, phase angle and Angular velocity come into play a lot with complex impedance.
calculus
asked Dec 2 at 20:34
Danny Sebahar
11
EDIT:A computer calculates it by closing in on the value of the angle after iterating (+/-pi)/(Some constant). A user posted a link to the CORDIC method wiki but I can't understand it still after a day.
I tested the series expansion with a bunch of angles and close in on the angle after very iterations of the series:
Here I used Excel's Trig functions to find Sin, cos, tan, csc, sec, & tan for ".6" Radians. Using the Y=sin(y), & X=cos(x), & m=tan(y/x) I close in on the value of ARCTAN(Y/X) quickly and reliably.
Original Question:
I was thinking of this problem:
Given a Unit Circle and a line from the origin through it's circumference at some point where the X value is known but not the Y value find the Y-value.
You can use the pythagorean theorem to find Y or you can use ARCCOS(x) to get the angle "A" and then solve sin(A) to get the Y-value.
So I was in Excel and the Inverse Trig functions aren't available functions in MS Excel. So I made a "Look-Up-Table" of the Cosine of Angles 0-90 down to the third decimal point.
This made me wonder if it was possible to calculate ARCSIN, ARCCOS, or ARCTAN using mathematical formulas and logic. I then figured MS Excel didn't have them as functions because that would require huge LUTs to be loaded into the memory every time Excel is opened as being accurate to the 3rd decimal takes tens of thousands of cells. So I figured they just don't allow those functions.
I then read on wikipedia that they can be derived but it didn't explain. Does anyone know if the inverse trig functons can be derived with a mathematical proof or are they simply "arcsin(y)=the angle that a ray from the origin must be in order for it to cross the Circumference of a circle at a right angle at a point with a y-value of "y""?
This seems electronic enough because waveforms, frequency, phase angle and Angular velocity come into play a lot with complex impedance.
calculus
calculus
asked Dec 2 at 20:34
Danny Sebahar
11
asked Dec 2 at 20:34
Danny Sebahar
11
asked Dec 2 at 20:34
Danny Sebahar
11
asked Dec 2 at 20:34
Danny Sebahar
11
asked Dec 2 at 20:34
Danny Sebahar
11
11
migrated from electronics.stackexchange.com Dec 9 at 4:00
This question came from our site for electronics and electrical engineering professionals, students, and enthusiasts.
migrated from electronics.stackexchange.com Dec 9 at 4:00
This question came from our site for electronics and electrical engineering professionals, students, and enthusiasts.
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
1
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22
|
show 2 more comments
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
1
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
1
1
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22
|
show 2 more comments
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031987%2fcan-the-inverse-trigonometric-functions-be-calculated-without-look-up-tables%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031987%2fcan-the-inverse-trigonometric-functions-be-calculated-without-look-up-tables%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
What are ACOS, ASIN, ATAN, and ATAN2 in Excel if not inverse trigonometric functions?
– Andrew Morton
Dec 2 at 20:39
1
I'm voting to close this question as off-topic because it belongs on Math.SE
– brhans
Dec 2 at 20:40
This is a math question. Voting to close. Please note that excel DOES have inverse trig functions. ASIN, ACOS and two versions of inverse tangent, ATAN and ATAN2.
– mkeith
Dec 2 at 20:41
I know, but about the calculator, how else would it do it? I can't imagine any other way that a computer can take the x or y value of a point on a circles circumference and return it's angle. I'm gobsmacked and have been for years on this. (Inverse Trig Functions I use for Filter Capacitor sizing when rectifying AC to a steady ripple free DC, if I want 5% Ripple max that gives me my Y-value -Voltage- and I get the change in Timeusing Arcsin to get the angle in degrees, subtract the previous angle of Peak Voltage -90 degrees- for the equation C=I(dT/dV).
– Danny Sebahar
Dec 2 at 21:01
@DannySebahar Like Bimpelrekkie said, CORDIC. Look at the link they gave.
– Hearth
Dec 2 at 21:22