Maths Trignometric function
Hello guys this is my first time posting here.I need help to understand the question and the answer I have posted in the images.I need to know what this question is asking and how is the question being solved.I know trignometric functions but do not know how to solve these type of trignometric questions.I will be solving these types of questions in my exams.I am waiting for your answers so I can learn.Thanks!
trigonometry
edited Dec 10 '18 at 0:10
gimusi
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
|
show 5 more comments
Hello guys this is my first time posting here.I need help to understand the question and the answer I have posted in the images.I need to know what this question is asking and how is the question being solved.I know trignometric functions but do not know how to solve these type of trignometric questions.I will be solving these types of questions in my exams.I am waiting for your answers so I can learn.Thanks!
trigonometry
edited Dec 10 '18 at 0:10
gimusi
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
3
Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06
|
show 5 more comments
Hello guys this is my first time posting here.I need help to understand the question and the answer I have posted in the images.I need to know what this question is asking and how is the question being solved.I know trignometric functions but do not know how to solve these type of trignometric questions.I will be solving these types of questions in my exams.I am waiting for your answers so I can learn.Thanks!
trigonometry
edited Dec 10 '18 at 0:10
gimusi
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
Hello guys this is my first time posting here.I need help to understand the question and the answer I have posted in the images.I need to know what this question is asking and how is the question being solved.I know trignometric functions but do not know how to solve these type of trignometric questions.I will be solving these types of questions in my exams.I am waiting for your answers so I can learn.Thanks!
trigonometry
trigonometry
edited Dec 10 '18 at 0:10
gimusi
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
edited Dec 10 '18 at 0:10
gimusi
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
edited Dec 10 '18 at 0:10
gimusi
1
edited Dec 10 '18 at 0:10
gimusi
1
edited Dec 10 '18 at 0:10
gimusi
1
1
asked Dec 9 '18 at 23:54
Faisal Khawar
11
asked Dec 9 '18 at 23:54
Faisal Khawar
11
asked Dec 9 '18 at 23:54
Faisal Khawar
11
11
3
Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06
|
show 5 more comments
3
Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06
3
3
Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06
|
show 5 more comments
1 Answer
1
active
oldest
votes
For a problem like this, I like to make a quick substitution: $x = costheta$. Then,
$$2 cos^2 theta - costheta = 0 ;;; text{becomes} ;;; 2x^2 - x = 0$$
Solve for $x$ in this latter equation to get some solutions.
So say your solutions were hypothetically $x = 1$ and $x=0$ (note: these are hypothetical solutions to an equation, not necessarily solutions to the one above). Then, remembering $x = cos theta$,
$$x = 1 ;;; text{means} ;;; cos theta = 1$$
$$x = 0 ;;; text{means} ;;; cos theta = 0$$
From there, you want to find which $theta$ in the interval in the problem yield the values you found. (Don't forget that $costheta$ and other related functions are periodic, which may prove helpful sometimes. So if $cos (theta) =1$, so does $cos (theta + 2pi)$, for example.)
Plugging in the values for $theta$ you find into the original equation will also prove helpful to double-check them. (I forget if this method introduces extraneous solutions. I don't think it does but I could be wrong. Regardless, checking solutions like this is always a good paranoia check.)
If none of the values in the given interval yield a solution to the equation, then you say the solution set is $emptyset$: this means "this solution set is empty," or equivalently "there are no solutions."
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
add a comment |
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For a problem like this, I like to make a quick substitution: $x = costheta$. Then,
$$2 cos^2 theta - costheta = 0 ;;; text{becomes} ;;; 2x^2 - x = 0$$
Solve for $x$ in this latter equation to get some solutions.
So say your solutions were hypothetically $x = 1$ and $x=0$ (note: these are hypothetical solutions to an equation, not necessarily solutions to the one above). Then, remembering $x = cos theta$,
$$x = 1 ;;; text{means} ;;; cos theta = 1$$
$$x = 0 ;;; text{means} ;;; cos theta = 0$$
From there, you want to find which $theta$ in the interval in the problem yield the values you found. (Don't forget that $costheta$ and other related functions are periodic, which may prove helpful sometimes. So if $cos (theta) =1$, so does $cos (theta + 2pi)$, for example.)
Plugging in the values for $theta$ you find into the original equation will also prove helpful to double-check them. (I forget if this method introduces extraneous solutions. I don't think it does but I could be wrong. Regardless, checking solutions like this is always a good paranoia check.)
If none of the values in the given interval yield a solution to the equation, then you say the solution set is $emptyset$: this means "this solution set is empty," or equivalently "there are no solutions."
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
add a comment |
For a problem like this, I like to make a quick substitution: $x = costheta$. Then,
$$2 cos^2 theta - costheta = 0 ;;; text{becomes} ;;; 2x^2 - x = 0$$
Solve for $x$ in this latter equation to get some solutions.
So say your solutions were hypothetically $x = 1$ and $x=0$ (note: these are hypothetical solutions to an equation, not necessarily solutions to the one above). Then, remembering $x = cos theta$,
$$x = 1 ;;; text{means} ;;; cos theta = 1$$
$$x = 0 ;;; text{means} ;;; cos theta = 0$$
From there, you want to find which $theta$ in the interval in the problem yield the values you found. (Don't forget that $costheta$ and other related functions are periodic, which may prove helpful sometimes. So if $cos (theta) =1$, so does $cos (theta + 2pi)$, for example.)
Plugging in the values for $theta$ you find into the original equation will also prove helpful to double-check them. (I forget if this method introduces extraneous solutions. I don't think it does but I could be wrong. Regardless, checking solutions like this is always a good paranoia check.)
If none of the values in the given interval yield a solution to the equation, then you say the solution set is $emptyset$: this means "this solution set is empty," or equivalently "there are no solutions."
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
add a comment |
For a problem like this, I like to make a quick substitution: $x = costheta$. Then,
$$2 cos^2 theta - costheta = 0 ;;; text{becomes} ;;; 2x^2 - x = 0$$
Solve for $x$ in this latter equation to get some solutions.
So say your solutions were hypothetically $x = 1$ and $x=0$ (note: these are hypothetical solutions to an equation, not necessarily solutions to the one above). Then, remembering $x = cos theta$,
$$x = 1 ;;; text{means} ;;; cos theta = 1$$
$$x = 0 ;;; text{means} ;;; cos theta = 0$$
From there, you want to find which $theta$ in the interval in the problem yield the values you found. (Don't forget that $costheta$ and other related functions are periodic, which may prove helpful sometimes. So if $cos (theta) =1$, so does $cos (theta + 2pi)$, for example.)
Plugging in the values for $theta$ you find into the original equation will also prove helpful to double-check them. (I forget if this method introduces extraneous solutions. I don't think it does but I could be wrong. Regardless, checking solutions like this is always a good paranoia check.)
If none of the values in the given interval yield a solution to the equation, then you say the solution set is $emptyset$: this means "this solution set is empty," or equivalently "there are no solutions."
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
For a problem like this, I like to make a quick substitution: $x = costheta$. Then,
$$2 cos^2 theta - costheta = 0 ;;; text{becomes} ;;; 2x^2 - x = 0$$
Solve for $x$ in this latter equation to get some solutions.
So say your solutions were hypothetically $x = 1$ and $x=0$ (note: these are hypothetical solutions to an equation, not necessarily solutions to the one above). Then, remembering $x = cos theta$,
$$x = 1 ;;; text{means} ;;; cos theta = 1$$
$$x = 0 ;;; text{means} ;;; cos theta = 0$$
From there, you want to find which $theta$ in the interval in the problem yield the values you found. (Don't forget that $costheta$ and other related functions are periodic, which may prove helpful sometimes. So if $cos (theta) =1$, so does $cos (theta + 2pi)$, for example.)
Plugging in the values for $theta$ you find into the original equation will also prove helpful to double-check them. (I forget if this method introduces extraneous solutions. I don't think it does but I could be wrong. Regardless, checking solutions like this is always a good paranoia check.)
If none of the values in the given interval yield a solution to the equation, then you say the solution set is $emptyset$: this means "this solution set is empty," or equivalently "there are no solutions."
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
answered Dec 10 '18 at 0:37
Eevee Trainer
4,6021634
4,6021634
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
add a comment |
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
I am sorry I do not understand.If you could solve the problem if posted step by step it would be helpful.
– Faisal Khawar
Dec 10 '18 at 3:42
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
@FaisalKhawar What in particular don't you understand? We usually discourage line-by-line answers since they don't let the OP think for themselves.
– Toby Mak
Dec 20 '18 at 13:25
add a comment |
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Welcome! We'll be glad to help you but you should present the question in a proper way. You should indeed use MathJax and explain you r work and effort on it. Refer also to How to ask a good question.
– gimusi
Dec 9 '18 at 23:58
Please try to improve that otherwise soon your question will be downvoted, closed and then deleted.
– gimusi
Dec 9 '18 at 23:59
What is $phi$ in your image?
– YiFan
Dec 10 '18 at 0:00
Hello how should I improve my question?
– Faisal Khawar
Dec 10 '18 at 0:02
@FaisalKhawar Read the link given and this one to format the question properly in MathJax MathJax basic tutorial and quick reference.
– gimusi
Dec 10 '18 at 0:06