Chapter SH, Problem 13.1EP

To determine

To find:

The each expression into trigonometric form

Answer to Problem 13.1EP

The exact value of $\sin \theta =\frac{4}{5}$

Explanation of Solution

Given:

  $\cos \theta =\frac{3}{5};0^0<\theta <{90}^0$

Concept used:

Trigonometric ratios: - Atrigonometric ratio are the ratios between edges of a right triangle.

Calculation:

Trigonometric ratio is

  $\begin{array}{l}\cos \theta =\frac{3}{5};0^0<\theta <{90}^0\\ \sin \theta =\sqrt{1-{\cos }^2\theta }\\ \sin \theta =\sqrt{1-{\left(\frac{3}{5}\right)}^2}\\ \sin \theta =\sqrt{1-\frac{9}{25}}\\ \sin \theta =\sqrt{\frac{16}{25}}\\ \sin \theta =\frac{4}{5}\end{array}$