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Original post by m_ezi

Solve 2tan^2 theta = 15tan theta - 7 in the interval - 180 deg < theta < 360 deg Give your solution(s) correct to 2 decimal places where appropriate.

I have been able to figure out 4 solutions for the question above but the question requires 6.

Please help!!

I have been able to figure out 4 solutions for the question above but the question requires 6.

Please help!!

Post what you've done - we will help

Original post by Muttley79

Post what you've done - we will help

So i let tantheta = x (like a quadratic)

then I made the equation equal to 0 :

2x^2 - 15x + 7

then i factorised normally (2x-1) (x-7)

then i got two solutions to be : 1/2 and 7 then substituting tan back in:

tanx = 1/2

i got x= 26.57

then using the cast diagram i got another solution to be : x= 206.57 (2dp)

then for tanx = 7

i got x= 81.87(2dp)

then using the cast diagram, my other solution was :

261.87

so as you can see my four solutions were:

26.57,206.57,81.87 and 261.87

but the question requires six solutions?!

Original post by m_ezi

So i let tantheta = x (like a quadratic)

then I made the equation equal to 0 :

2x^2 - 15x + 7

then i factorised normally (2x-1) (x-7)

then i got two solutions to be : 1/2 and 7 then substituting tan back in:

tanx = 1/2

i got x= 26.57

then using the cast diagram i got another solution to be : x= 206.57 (2dp)

then for tanx = 7

i got x= 81.87(2dp)

then using the cast diagram, my other solution was :

261.87

so as you can see my four solutions were:

26.57,206.57,81.87 and 261.87

but the question requires six solutions?!

then I made the equation equal to 0 :

2x^2 - 15x + 7

then i factorised normally (2x-1) (x-7)

then i got two solutions to be : 1/2 and 7 then substituting tan back in:

tanx = 1/2

i got x= 26.57

then using the cast diagram i got another solution to be : x= 206.57 (2dp)

then for tanx = 7

i got x= 81.87(2dp)

then using the cast diagram, my other solution was :

261.87

so as you can see my four solutions were:

26.57,206.57,81.87 and 261.87

but the question requires six solutions?!

What about the rest of the range? Aren't there more solutions between -180 and 0

Original post by Muttley79

What about the rest of the range? Aren't there more solutions between -180 and 0

thats what Im stuck on , i dont know how to find the negative solutions

Original post by m_ezi

thats what Im stuck on , i dont know how to find the negative solutions

Go in the other direction on your cast diagram, past zero, and into the negatives.

Original post by sound-famous-

Go in the other direction on your cast diagram, past zero, and into the negatives.

whyy?

Original post by m_ezi

whyy?

Thats how you get the negative solutions. Since tan (and sin and cos) are periodic, there are an infinite number of solutions that occur at regular intervals. Imagine a tan graph that goes on forever to negative and positive infinity, there will be infinitely many solutions in each direction. By going backwards on your cast diagram you can find the negative solutions. Put them in your calculator and see that it gives the same answer as the positive solutions.

Original post by sound-famous-

Thats how you get the negative solutions. Since tan (and sin and cos) are periodic, there are an infinite number of solutions that occur at regular intervals. Imagine a tan graph that goes on forever to negative and positive infinity, there will be infinitely many solutions in each direction. By going backwards on your cast diagram you can find the negative solutions. Put them in your calculator and see that it gives the same answer as the positive solutions.

do i subtract 360 or 180 to find the negative values

Original post by m_ezi

do i subtract 360 or 180 to find the negative values

What does the graph look like? That will give you your answer ...

Remember you can always check by substitution.

Original post by Muttley79

What does the graph look like? That will give you your answer ...

Remember you can always check by substitution.

Remember you can always check by substitution.

i didnt use a graph it was a cast diagram

Original post by m_ezi

i didnt use a graph it was a cast diagram

CAST comes from the graph! You need to be flexible in the way you tackle questions

Original post by Muttley79

is this for the values?

Original post by Muttley79

i have not seen this before and im currently doing gcse fm 😭

Original post by m_ezi

i have not seen this before and im currently doing gcse fm 😭

Really? The graphs are part of GCSE!

Original post by Muttley79

Really? The graphs are part of GCSE!

well i think we will learn this later on in the year , but ill read more on it , but the question i have is if they also want values for negative theta, how do i use the CAST diagram to find the solutions that are also negative?

Original post by m_ezi

well i think we will learn this later on in the year , but ill read more on it , but the question i have is if they also want values for negative theta, how do i use the CAST diagram to find the solutions that are also negative?

You go round the CAST diagram clockwise [-ve turn] from 0 and will see that tan is +ve between -90 and -180 [see link with graph]

Can you find the angles now?

Original post by Muttley79

You go round the CAST diagram clockwise [-ve turn] from 0 and will see that tan is +ve between -90 and -180 [see link with graph]

Can you find the angles now?

Can you find the angles now?

do i go round the cast diagram clockwise from the principal value?

Original post by m_ezi

do i go round the cast diagram clockwise from the principal value?

You could do that but the angle only becomes -ve at zero.

Why have you been set this question if you haven't covered this?

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