Finding Exact Values for Trigonometric Functions

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To find the exact values of tan 510, sin (-315), and sin 750, one can use periodic properties of trigonometric functions. For tan 510, it simplifies to tan 150 degrees, while sin (-315) equals sin 45 degrees, and sin 750 simplifies to sin 30 degrees. The discussion also highlights the importance of distinguishing between -√3/2 and -√3/2 for solving sin θ = -√3/2, noting that the correct angles in the third and fourth quadrants are 240 degrees and 300 degrees. Understanding the unit circle and the periodic nature of trigonometric functions is essential for solving these problems accurately.
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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.
 
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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.
 
GLprincess02 said:
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!
 
You're right, I just realized my mistake. It should have said "-\frac{\sqrt{3}}{2}."
 

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