Chapter 4, Problem 43RE

To determine

Value of the six trigonometric functions of the angle for the given point.

Answer to Problem 43RE

So, value of six trigonometric functions for the given point is

  $\sin \theta =\frac{4}{5},\cos \theta =\frac{3}{5},\tan \theta =\frac{4}{3},\csc \theta =\frac{5}{4},\sec \theta =\frac{5}{3}\text{and}\cot \theta =\frac{3}{4}$

Explanation of Solution

Given:

The given point is (12, 16) which is the terminal side of the angle in the standard position.

From the given point,

As, for the right angled triangle,

  $\begin{array}{l}\text{r}=\sqrt{{12}^2+{16}^2}\\ =\sqrt{144+256}\\ =20\end{array}$

So,

For right angled triangle perpendicular=16, base=12 and hypotenuse=20

Therefore,

  $\begin{array}{l}\sin \theta =\frac{16}{20}\\ =\frac{4}{5}\\ \cos \theta =\frac{12}{20}\\ =\frac{3}{5}\\ \tan \theta =\frac{16}{12}\\ =\frac{4}{3}\\ \csc \theta =\frac{5}{4}\\ \sec \theta =\frac{5}{3}\\ \cot \theta =\frac{3}{4}\end{array}$