Chapter 12.1, Problem 2CYU

To determine

Calculate the values of six trigonometric functions for angle $\theta$ .

Answer to Problem 2CYU

The all the values of trigonometric functions are $\sin \theta =\frac{10.6}{16},\cos \theta =\frac{12}{16},\tan \theta =\frac{10.6}{12},\csc \theta =\frac{16}{10.6},\sec \theta =\frac{16}{12},\cot \theta =\frac{12}{10.6}$ .

Explanation of Solution

Given:

It is given in the question that the figure is given below in which b and h are given:

  

Concept Used:

In this, use the concept of pythgoras theorem and trigonometric ratios and the formula will be $h^2=p^2+b^2$ , $\sin \theta =\frac{p}{h},\cos \theta =\frac{b}{h},\tan \theta =\frac{p}{b},\csc \theta =\frac{h}{p},\sec \theta =\frac{h}{b},\cot \theta =\frac{b}{p}$ .

Calculation: Here, use Pythagoras theorem where $b=12,h=16$ .

  $\begin{array}{l}{h}^2=p^2+b^2\\ {16}^2=p^2+{12}^2\\ p^2=256-144\\ p^2=112\\ p=\sqrt{112}=10.6\end{array}$

Now, use the trigonometric ratios:

  $\sin \theta =\frac{10.6}{16},\cos \theta =\frac{12}{16},\tan \theta =\frac{10.6}{12},\csc \theta =\frac{16}{10.6},\sec \theta =\frac{16}{12},\cot \theta =\frac{12}{10.6}$

Conclusion:

The all the values are $\sin \theta =\frac{10.6}{16},\cos \theta =\frac{12}{16},\tan \theta =\frac{10.6}{12},\csc \theta =\frac{16}{10.6},\sec \theta =\frac{16}{12},\cot \theta =\frac{12}{10.6}$ .