State an equivalent expression for sin (-7pi/6) in terms of the related acute angle.

I don't really know how to solve these kind of questions, I find everything I google doesn't explain how to do it :(

- Nov 27th 2009, 06:31 AMkmjtEquivalent expression for sin(-7pi/6) in terms of the related acute angle.
State an equivalent expression for sin (-7pi/6) in terms of the related acute angle.

I don't really know how to solve these kind of questions, I find everything I google doesn't explain how to do it :( - Nov 27th 2009, 06:59 AMmathaddict
- Nov 27th 2009, 07:25 AMkmjt
I'm not following =/ I know that sin (-7pi/6) is the same thing as sin (-210 degrees) but i'm not sure where to go from there. I'm not even sure what the question is asking (Worried)

- Nov 27th 2009, 07:34 AMmathaddict
OK , try to follow here . I will go slow .

$\displaystyle \sin (-210)=-\sin 210$ (Step 1)

$\displaystyle -\sin 210=-(-\sin 30)$ (Step 2)

This is because sin is negative in the 3rd quadrant .

$\displaystyle -(-\sin 30)=\sin 30$ (Step 3)

I think this is what the question wants since it asks for acute angles (angle < than 90 degree)

If you still have any problem , just indicate which step you are unsure with .. don say everything or else i don know where to start . - Nov 27th 2009, 08:01 AMkmjt
Where is the-(-sin30) coming from?

- Nov 27th 2009, 08:05 AMmathaddict
- Nov 27th 2009, 08:12 AMkmjt
It just clicked in my brain thanks!

- Nov 27th 2009, 06:35 PMHallsofIvy
I don't see why degrees should be easier than radians and I think it is good to encourage people to think in terms of radians. $\displaystyle \frac{7\pi}{6}= \pi+ \frac{\pi}{6}$. Since the angle is negative, we swing

**down**from the positive x axis to the negative y axis and then [itex]\pi/6[/itex] above. Now we are in the second quadrant where sine is still postive.

$\displaystyle sin(-\frac{7\pi}{6})= sin(\frac{\pi}{6})$.