Question

Find the exact value of each trigonometric function.

sin(θ)= 3/5
cos(θ)= 4/5
tan(θ)= 3/4

1. cos(2θ)=
2. tan(2θ)=
3. cot(2θ)=
4. sec(2θ )=
5. csc(2θ)=

Answer 1

You are given all 3 of the major trig ratios of Ø
(btw, you are dealing with the 3-4-5 Pythagorean triangle, the simplest of such triangles)

You must memorize or have at hand from your text or notes, the following:
sin (2Ø) = 2 sinØcosØ
cos(2Ø) = cos^2 Ø - sin^2 Ø
All the other double angle trig ratios can be easily derived from those two

I will do one of the, say #3
cot 2Ø = cos 2Ø/sin 2Ø
= (cos^2 Ø - sin^2 Ø)/(2sinØcosØ)
= (16/25 - 9/25)/(2(3/5)(4/5) )
= (7/25) / (24/25)
= (7/25)(25/24) = 7/24

let me know what you get for the others.

Answer 2

Hey, you have a textbook I suspect that shows the trig formulas you need
for example cos (2 T) = 2 cos^2 (T) - 1
or = cos^2(T) - sin^2 (T)

I am not going to do the arithmetic for you