Question

Given sec theta=-4/3 and 90°

Answer 1

Answer:

Option A.

Step-by-step explanation:

It is given secθ = - $\frac{4}{3}$

then cosθ = -$\frac{3}{4}$

Now we know the identity

sinθ = $\sqrt{1-cos^{2}\theta }$

       = $\sqrt{1-(-\frac{3}{4} )^{2}}$

       = $\frac{\sqrt{7} }{4}$

Now sin2θ = 2sinθcosθ

Now we put the values of cosine and sine in the formula

sin2θ = 2×(-$\frac{3}{4}$)($\frac{\sqrt{7}}{4}$)

         = -$\frac{3\sqrt{7}}{8}$

Therefore, option A. is the answer.