Chapter 4, Problem 52CR

(a).

To determine

To calculate: the value of trigonometric function using calculator.

Answer to Problem 52CR

Value of trigonometric function $\tan \left(\frac{9\pi }{20}\right)$ is $\underset{\_}{6.3137}$ .

Explanation of Solution

Given information:

Trigonometric function whose value needs to be determined is as follows.

  $\tan \left(\frac{9\pi }{20}\right)$

Formula used:

  $\pi ={180}^{\circ }$

Calculation:

Trigonometric function is $\tan \left(\frac{9\pi }{20}\right)$ .

To use degree mode of calculator, convert complete angle into degree.

  $\frac{9\pi }{20}=\frac{9}{20}\times {180}^{\circ }$

  $=9\times 9^{\circ }$

  $={81}^{\circ }$

Calculate value of $\tan {81}^{\circ }$ using calculator in degree mode.

  $\tan {81}^{\circ }=6.31375\approx 6.3137$

Value of trigonometric function $\tan \left(\frac{9\pi }{20}\right)$ is $\underset{\_}{6.3137}$ .

(b).

To determine

To calculate: the value of trigonometric function using calculator.

Answer to Problem 52CR

Value of trigonometric function $\cot \left(\frac{9\pi }{20}\right)$ is $\underset{\_}{0.1584}$ .

Explanation of Solution

Given information:

Trigonometric function whose value needs to be determined is as follows.

  $\cot \left(\frac{9\pi }{20}\right)$

Formula used:

  $\pi ={180}^{\circ }$

Calculation:

Trigonometric function is $\cot \left(\frac{9\pi }{20}\right)$ .

To use degree mode of calculator, convert complete angle into degree.

  $\frac{9\pi }{20}=\frac{9}{20}\times {180}^{\circ }$

  $=9\times 9^{\circ }$

  $={81}^{\circ }$

Calculate value of $\cot {81}^{\circ }$ using calculator in degree mode.

  $\cot {81}^{\circ }=0.15838\approx 0.1584$

Value of trigonometric function $\cot \left(\frac{9\pi }{20}\right)$ is $\underset{\_}{0.1584}$ .