# Math Help - Trigonometry help with identities

1. ## Trigonometry help with identities

I'm not sure if you call them identities but can someone please help me with a question?

tanx = (-4.3315) when 360 ≤ x ≤ 720

This is what I did:
inverse tan (-4.3315) + 540 deg.

I'm not sure where the 540 degrees came from, though.
Your help would be much appreciated!

2. Originally Posted by averageperson12345678
I'm not sure if you call them identities but can someone please help me with a question?

tanx = (-4.3315) when 360 ≤ x ≤ 720

This is what I did:
inverse tan (-4.3315) + 540 deg.

I'm not sure where the 540 degrees came from, though.
Your help would be much appreciated!
understand that the inverse tangent function only yields values between -90 and +90 degrees, and angles that differ by 180 degrees have the same tangent value.

using a calculator in degree mode, note that $\tan^{-1}(-4.3315)$ is very close to $-77^\circ$.

since the angle you want is between 360 and 720, add successive multiples of 180 ...

-77+180 = 103 ... not large enough

-77 + 360 = 283 ... not there, yet

-77 + 540 = 463 ... ok, but there is another

-77 + 720 = 643

so, note you get two valid solutions in the desired range. 463 and 643 degrees.

take the tangent of both angles in your calculator to confirm.

3. Thank you so much for that explanation! Trig is not exactly my strength. haha xD

Thank you again! That was very helpful

4. Originally Posted by skeeter
understand that the inverse tangent function only yields values between -90 and +90 degrees, and angles that differ by 180 degrees have the same tangent value.

using a calculator in degree mode, note that $\tan^{-1}(-4.3315)$ is very close to $-77^\circ$.

since the angle you want is between 360 and 720, add successive multiples of 180 ...

-77+180 = 103 ... not large enough

-77 + 360 = 283 ... not there, yet

-77 + 540 = 463 ... ok, but there is another

-77 + 720 = 643

so, note you get two valid solutions in the desired range. 463 and 643 degrees.

take the tangent of both angles in your calculator to confirm.

Thank you! Is it the same concept for sinx = (-.9397)?
I have the answers and I have a way of solving it but I'm not sure if it's the correct way.
I came up with 610, 650.

I'm so sorry for all these questions. Trig is not exactly my strength.

5. Originally Posted by averageperson12345678
Thank you! Is it the same concept for sinx = (-.9397)?
I have the answers and I have a way of solving it but I'm not sure if it's the correct way.
I came up with 610, 650.

I'm so sorry for all these questions. Trig is not exactly my strength.

the value of sine is negative in quads III and IV, so not exactly the same as tangent ... tangent is negative in quads II and IV.