Chapter 5, Problem 10RE

(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 10RE

The exact value is $0.80901$ .

Explanation of Solution

Given: $\mathrm{Cos}\frac{\text{π}}{5}$

Concept used:

  ${\text{πradian=180}}^{\text{0}}$ .

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

In 1^stquadrant $\text{Cosθ}$ is positive.

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

Calculation:

  $\mathrm{Cos}\frac{\text{π}}{5}$ = ${\text{sin36}}^0$ so, the angle lies in 1st quadrant.

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

  $\mathrm{Cos}\frac{\text{π}}{5}$ can be written as $\mathrm{Cos}{36}^0$ .

  $\mathrm{Cos}{36}^0=0.80901$ .

Hence the exact value is ${\text{Cos36}}^0=\mathrm{0.80901.}$ .

(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 10RE

The exact value is $\mathrm{0.80901.}$

Explanation of Solution

Given: $\mathrm{Cos}\left(-\frac{\pi }{5}\right)$ .

Concept used:In 4^thquadrant $\text{Cosθ}$ is positive.

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

Calculation:

  $\mathrm{Cos}\left(-\frac{\pi }{5}\right)$ = $\text{Cos}\left({\text{-36}}^0\right)$ so, the angle lies in 4th quadrant.

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

  $\mathrm{Cos}\left(-\frac{\pi }{5}\right)$ can be written as $\text{Cos}\left({\text{-36}}^0\right)$

  $\text{Cos}\left({\text{-36}}^0\right)=\mathrm{0.80901.}$

Hence the exact value is $\mathrm{0.80901.}$