Question

Given sin x = a/2 and tanx< 0 find cos x

Answer 1

Answer:

cosθ = ( √4 - a² ) ÷ 2

Explanation:

sinθ = a/2

according to sincostan rule:

sinθ = opposite/ hypotenuse

cosθ = adjacent/ hypotenuse

so here opposite is a and hypotenuse is 2

adjacent² + opposite² = hypotenuse²

adjacent² + a² = 2²

adjacent = √4 - a²

we found our adjacent.

so cosθ = adjacent/ hypotenuse

             =  ( √4 - a² ) / 2

so cosθ = $\frac{ \sqrt{4 - a^{2}} }{2}$