Chapter 5, Problem 11RE

(a)

To determine

To find: Theexact value of trigonometric function if not possible use a calculator and correct up-to five decimal places.

Answer to Problem 11RE

Theexact value is 0.

Explanation of Solution

Given: $\mathrm{Cos}\frac{\text{9π}}{2}$ .

Concept used:

  ${\text{πradian=180}}^{\text{0}}$ .

  $\text{1radian=}\frac{{\text{180}}^{\text{0}}}{\text{π}}$ .

In second quadrant $\text{Sinθ}$ is positive.

Since, its changing horizontally the trigonometric doesn’t change $\text{Sinθ}$ to $\text{Cosθ}$ it remains same.

Calculation:

  $\mathrm{Cos}\frac{\text{9π}}{2}$ = ${\text{Cos810}}^0$ so, the angle lies in vertical line.

Actually, the angle can be measured directly by unit circle, let’s solved it without the use of unit circle.

  $\mathrm{Cos}\frac{\text{9π}}{2}$ can be written as $\cos \left(\text{4π+}\frac{\text{π}}{2}\right)$

  $\text{Cos}\left(\text{4π+}\frac{\text{π}}{2}\right)\text{=Cos}\frac{\text{π}}{2}=0.$

Hence the exact value is 0.

(b)

To determine

To find:The exact value of trigonometric function if not possible use a calculator and correct up-to five decimal places.

Answer to Problem 11RE

Theexact value is $\infty .$

Explanation of Solution

Given: $\mathrm{Sec}\frac{\text{9π}}{2}$ .

Concept used: $\text{Secθ}$ lies in vertical line.

Since, its changing horizontally the trigonometric doesn’t change $\text{Cosθ}$ to $\text{Sinθ}$ it remains same.

Calculation:

  $\mathrm{Sec}\frac{\text{9π}}{2}$ = ${\text{Sec135}}^0$ so, the angle lies in vertical.

Actually, the angle can be measured directly by unit circle, let’s solved it without the use of unit circle.

  $\mathrm{Sec}\frac{\text{9π}}{2}$ can be written as $\mathrm{Sec}\left(\text{4π+}\frac{\text{π}}{2}\right)$

  $$

  $\mathrm{Sec}\left(\text{4π+}\frac{\text{π}}{2}\right)\text{=Sec}\frac{\text{π}}{2}=\frac{1}{0}=\infty .$

Hence the exact value is $\infty .$