Trigonometry Question

Question

Find sin2A and tanA/2?

given cotA=15/8 and A terminates in Quadrant 3

Answer 1

Given that cot(θ) = adjacent/opposite and, in this problem cot(A) = 15/8 with angle A terminating in Q3. we know that the adjacent side is -15 and the opposite side is -8 like this:

We can solve for h using the Pythagorean Theorem:

h = √((-8)² + (-15)²) = √(64 + 225) = √289 = 17

This means we can write trig ratios as follows:

sin(A) = -8/17

cos(A) = -15/17

tan(A) = 8/15

Using the double angle identity:

sin(2x) = 2sin(x)cos(x) we cans say:

sin(2A) = 2sin(A)cos(A) = 2(-8/17)(-15/17) = 240/289

So sin(2A) = 240/289

tan(2A) = 2tan(A)/(1 - tan²(A)) = 2(8/15)/(1 - (8/15)²) = (16/15)/(1 - 64/225) = (16/15)/(161/225) = (16/15)•(225/161) = 240/161

So tan(2A) = 240/161