Question

Consider this equation. cos(theta) = (-2√5)/5. If theta is an angle in quadrant II, what is the value of sin(theta)? NO LINKS!!!​

Answer 1

• In second quadrant sin and cosec are positive

$\\ \tt\hookrightarrow sin^2\theta=1-cos^2\theta$

$\\ \tt\hookrightarrow sin^2\theta=1-(\dfrac{-2\sqrt{5}}{5})^2$

$\\ \tt\hookrightarrow sin^2\theta=1-\dfrac{20}{25}$

$\\ \tt\hookrightarrow sin^2\theta=\dfrac{5}{25}$

$\\ \tt\hookrightarrow sin\theta=\dfrac{\sqrt{5}}{5}$

$\\ \tt\hookrightarrow sin\theta=\dfrac{1}{\sqrt{5}}$