Question

If sin θ= 1/4, 0<θ<π/2, find the exact value of the following: sin(2θ), cos(2θ), sin(θ/2), cos(θ/2).

Answer 1

\[\sin2\theta = 2\sin \theta.\cos \theta\]
\[\cos2\theta=1-2\sin^2 \theta\]
\[\sin ^2\frac{ \theta }{ 2 }=\frac{ 1-\cos \theta }{ 2 }\]
\[\cos^2\frac{ \theta }{ 2 }\]
first find cos theta value and plug these values in formulas