Find sin(2x), cos(2x), and tan(2x) from the given information.

Question

sin(x) = − 3/5 for 3𝜋 2 < x < 2𝜋

sin(2x)=

cos(2x)=

tan(2x)=

Answer 1

If sin(x) = − 3/5 and you are in Q4 (between 3π/2 and 2π) then a sketch would look like this:

We can use the Pythagorean Theorem to solve for the missing side that I labeled as "adj":

(-3)² + (adj)² = 5²

adj = 4

Therefore cos(x) = 4/5 and tan(x) = -3/4. Of course we are given that sin(x) = -3/5

We now have enough information to use the double angle identities:

cos(2x) = cos²(x) – sin²(x)

sin(2x) = 2sin(x)cos(x)

tan(2x) = (2tan(x))/(1 - tan²(x))

So just plug in the values and simplify.