Question

If $\sin \theta =\frac{1}{\sqrt{2}}$, find all other trigonometric ratios of angle θ.

Answer 1

Given:

We have to find all the trigonometric ratios.

We have the following right angle triangle.

From the above figure,

$$\begin{gathered} \mathrm{Base}=\sqrt{{\mathrm{Hypotenuse}}^2-{\mathrm{Perpendicular}}^2} \\ \Rightarrow BC=\sqrt{A{C}^2-A{B}^2} \\ \Rightarrow BC=\sqrt{{\left(\sqrt{2}\right)}^2-1^2} \\ \Rightarrow BC=1 \end{gathered}$$