Suppose that sin(𝜃)=3/5 and 𝜃 is in the second quadrant. Use trigonometric identities to find the following quantities exactly.

Question

Find

cos(theta)

sin(2theta)

cos(2theta)

tan(2theta)

I found cos(theta) which is -4/5 but am not sure where to go from there.

Answer 1

Now that you have sinθ and cosθ, use the following trig identities to find the others:

sin(2θ) = 2 sinθcosθ (substitute in the values you already know)

cos(2θ) = (you actually have three identities to pick from--I will let you look them up)

tan(2θ) = sin(2θ)/cos(2θ) --once again substitute the values you found from the previous two answers)

Use the following to check your work:

desmos.com/calculator/hle0g7mdrw