Determine the Values?

Question

Suppose that θ is an angle in quadrant III. If the sine of the reference number for θ is 3/4, Use a right triangle to determine the values of the trigonometric functions of θ.

What? I am really lost on where to even start with this problem.

Please someone explain how to start this problem.

10 points! :]

Answer 1

Sorry if this is a bit wordy, it would be easier if I could draw you a diagram.

Using the unit circle (x^2 + y^2 =1), then we can find the sine and cosine of any angle by using the value of the point (x,y) on the circle

So if you have point A(x,y), origin O(0,0) and point B(1,0), then the angle determined by AOB has sin = y and cos = x.

So if you draw a circle with centre (0,0) with a reference angle in the first quadrant (call it β) which cuts through circle at point A(x,y), then

sin β = y = 3/4 (given)

cos β = x (you can figure this out, knowing (sin β)^2 + (cos β)^2 = 1)

Now draw the same angle in third quadrant, so θ = 180 + β (or π + β). By symmetry, you will see that this angle cuts through circle at point B(-x,-y)

Therefore

sin θ = -y = -sin β

cos θ = -x = -cos β

From these you can calculate tan, sec, csc