Chapter 4, Problem 51CR

(a).

To determine

To calculate: the value of trigonometric function using calculator.

Answer to Problem 51CR

Value of trigonometric function $\cos {84}^{\circ }$ is $\underset{\_}{1.1045}$ .

Explanation of Solution

Given information:

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

  $\cos {84}^{\circ }$

Calculation:

Trigonometric function is $\cos {84}^{\circ }$ .

Calculate value of $\cos {84}^{\circ }$ using calculator in degree mode.

  $\cos {84}^{\circ }=0.104528\approx 1.1045$

Value of trigonometric function $\cos {84}^{\circ }$ is $\underset{\_}{1.1045}$ .

(b).

To determine

To calculate: the value of trigonometric function using calculator.

Answer to Problem 51CR

Value of trigonometric function $\csc \left({52}^{\circ }12^{\prime }\right)$ is $\underset{\_}{1.2656}$ .

Explanation of Solution

Given information:

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

  $\csc \left({52}^{\circ }12^{\prime }\right)$

Formula used:

  $1^{\prime }={\left(\frac{1}{60}\right)}^{\circ }$

Calculation:

Trigonometric function is $\csc \left({52}^{\circ }12^{\prime }\right)$ .

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

  ${52}^{\circ }12^{\prime }={52}^{\circ }+12^{\prime }$

  $={52}^{\circ }+{\left(12\times \frac{1}{60}\right)}^{\circ }$

  $={52}^{\circ }+{\frac{1}{5}}^{\circ }$

  $={52.2}^{\circ }$

Calculate value of $\csc \left({52.2}^{\circ }\right)$ using calculator in degree mode.

  $\csc \left({52.2}^{\circ }\right)=1.26557\approx 1.2656$

Value of trigonometric function $\csc \left({52}^{\circ }12^{\prime }\right)$ is $\underset{\_}{1.2656}$ .