Question

Find the exact value of the sine and secant if the terminal side of theta passes through the point (8,-3)
Please explain!

Answer 1

Well, the coordinates help you come up with a triangle diagram that can be used to find the correct values. Recall that the sineof a triangle is the opposite side over the hypotenuse and that the secant of a triangle is the hypotenuse over the adjacent side. So with your coordinate we can draw this triangle:

Answer 2

Now both the sine and secant functions require us to find the value of x, which can be done with pythagorean theorem. You could find that x value, correct?

Answer 3

@awesomelady2

Answer 4

Yes, the value of x = sqrt73

Answer 5

Awesome. So now we just need to have opposite/hypotenuse and hypotenuse over adjacent. So for sine, we would have 3/sqrt(73) and for secant we would have sqrt(73)/8. Now the only issue is using the correct sign, positive or negative. Since sine represents y-values, would sine be positive or negative?

Answer 6

Positive, because: