Note that, \(\displaystyle{\csc{\theta}}=\) (Hypotenuse)/(Opposide side)

So Hypotenuse=21 and Opposite side=5.

Use Pythagorean theorem to find adjacent side as follows.

Adjacent side \(\displaystyle=\sqrt{{{21}^{{2}}-{5}^{{2}}}}\)

\(\displaystyle=\sqrt{{{441}-{25}}}\)

\(\displaystyle=\sqrt{{416}}\)

Sketch a right triangle for given trigonometric function.

Find the other five trigonometric function as follows.

\(\displaystyle{\sin{\theta}}=\) (Opposide side)/(Hypotenuse) \(\displaystyle=\frac{{5}}{{21}}\)

\(\displaystyle{\cos{\theta}}=\) (Adjacent side)/(Hypotenuse) \(\displaystyle=\frac{\sqrt{{416}}}{{21}}\)

\(\displaystyle{\tan{\theta}}=\) (Opposide side)/(Adjacent side) \(\displaystyle=\frac{{5}}{\sqrt{{416}}}\)

\(\displaystyle{\sec{\theta}}=\) (Hypotenuse)/(Adjacent side) \(\displaystyle=\frac{{21}}{\sqrt{{416}}}\)

\(\displaystyle{\cot{\theta}}=\) (Adjacent side)/(Opposide side) \(\displaystyle=\frac{\sqrt{{416}}}{{5}}\)

So Hypotenuse=21 and Opposite side=5.

Use Pythagorean theorem to find adjacent side as follows.

Adjacent side \(\displaystyle=\sqrt{{{21}^{{2}}-{5}^{{2}}}}\)

\(\displaystyle=\sqrt{{{441}-{25}}}\)

\(\displaystyle=\sqrt{{416}}\)

Sketch a right triangle for given trigonometric function.

Find the other five trigonometric function as follows.

\(\displaystyle{\sin{\theta}}=\) (Opposide side)/(Hypotenuse) \(\displaystyle=\frac{{5}}{{21}}\)

\(\displaystyle{\cos{\theta}}=\) (Adjacent side)/(Hypotenuse) \(\displaystyle=\frac{\sqrt{{416}}}{{21}}\)

\(\displaystyle{\tan{\theta}}=\) (Opposide side)/(Adjacent side) \(\displaystyle=\frac{{5}}{\sqrt{{416}}}\)

\(\displaystyle{\sec{\theta}}=\) (Hypotenuse)/(Adjacent side) \(\displaystyle=\frac{{21}}{\sqrt{{416}}}\)

\(\displaystyle{\cot{\theta}}=\) (Adjacent side)/(Opposide side) \(\displaystyle=\frac{\sqrt{{416}}}{{5}}\)