Finding Exact Values for Trigonometric Functions

[GLprincess02]

How can I go about finding the exact values of tan 510, sin (-315) and sin 750? I'm unsure of where to even begin on these problems and any help would be greatly appreciated.


Never mind, I found the answers to these problems. However, there is another problem on my homework the reads: "Find 2 values of $$\theta$$ such that 0 degrees < $$\theta$$ < 360 degrees and sin $$\theta$$ = -$$\sqrt{3/2}$$." I don't have a unit circle handy, so I'm unsure about how to solve it.

 

[PhyzicsOfHockey]

Sin is the y value so on a unit circle and why is negitive in quadrants 3 and 4. so at 240 deg and 300deg it should be that value.

 

[HallsofIvy]

How can I go about finding the exact values of tan 510, sin (-315) and sin 750? I'm unsure of where to even begin on these problems and any help would be greatly appreciated.


Never mind, I found the answers to these problems. However, there is another problem on my homework the reads: "Find 2 values of $$\theta$$ such that 0 degrees < $$\theta$$ < 360 degrees and sin $$\theta$$ = -$$\sqrt{3/2}$$." I don't have a unit circle handy, so I'm unsure about how to solve it.

tan(x) is periodic with period $\pi$ so surely it would help to note that 510= 2(180)+ 150= 3(180)- 30. Do you know sine and cosine of -30 degrees? -315= 2(180)- 45, and 750= 4(180)+ 30.

As for your second problem, did it say $-\sqrt{3/2}$ or $-\frac{\sqrt{3}}{2}$? That's an important difference!

 

[GLprincess02]

You're right, I just realized my mistake. It should have said "$-\frac{\sqrt{3}}{2}$."