Given sin of theta = -4/5, where 3*pi/2 is less than or equal to 0 is less than 2*pi, find the exact value for tan 2 theta

Answer 1

We have ξ in quadrant IV. Now tan2ξ = 2tanξ/(1 - tan²ξ);

Because sinξ = - 4/5, then cosξ = sqrt(1 - sin²ξ) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5 (cosξ > 0 in quadrant IV).

Now tanξ = sinξ/cosξ = (- 4/5)/(3/5) = - 4/3; tan2ξ = 2(- 4/3)/(1 - (-4/3)²) = (- 8/3)/(1 - 16/9)= (- 8/3)/(- 7/9) = 24/7.

Answer: tan2ξ = 24/7

Answer 2

Draw and label a diagram!

tan θ = -4/3

tan 2θ = (2 tan θθ) / (1 - tan² θ)

Can you substitute values for tan θ and answer?