Question

Please Help!!!!! If secθ = 4, then sinθ = _____.

Answer 1

Knowing that $\sec x=\dfrac{1}{\cos x}$:

$\sec\theta=4\iff\dfrac{1}{\cos\theta}=4\iff\cos\theta=\dfrac{1}{4}$

Using that $\sin^2x+\cos^2x=1$:

$\sin^2\theta+(\dfrac{1}{4})^2=1\iff \sin^2\theta=\dfrac{15}{16}\iff\\\\\boxed{\sin\theta=\pm\dfrac{\sqrt{15}}{4}}$