Chapter 8.6, Problem 7CE

a.

To determine

To calculate : the sine of a given angle

Answer to Problem 7CE

  $\sin 24°=0.4067$

Explanation of Solution

Given Information: sin 24⁰

Calculation :

Using the results of sine values of various angles in page 311, the value of given function is obtained as,

  $\sin 24°=0.4067$

b.

To determine

To calculate : the cosine of a given angle

Answer to Problem 7CE

  $\cos 57°$

  $=0.5446$

Explanation of Solution

Given Information: cos 57⁰

Calculation :

Using the results of cosine values of various angles in page 311, the value of given function is obtained as,

  $\cos 57°=0.5446$

c.

To determine

To calculate : the sine of a given angle

Answer to Problem 7CE

  $\sin 87°$

  $=0.9986$

Explanation of Solution

Given Information: sin 87⁰

Calculation:

Using the results of sine values of various angles in page 311, the value of given function is obtained as,

  $\sin 87°=0.9986$

d.

To determine

To calculate : the inverse cosine of a given value.

Answer to Problem 7CE

  ${\cos }^{-1}\left(0.9659\right)=15°$

Explanation of Solution

Given Information: The value 0.9659

Calculation:

Using the results of cosine values of various angles in page 311, the value of inverse of given value is obtained as,

  ${\cos }^{-1}\left(0.9659\right)=15°$

e.

To determine

To calculate: the inverse sine of a given value.

Answer to Problem 7CE

  ${\sin }^{-1}\left(0.1045\right)=6°$

Explanation of Solution

Given Information: The value 0.1045

Calculation:

Using the results of sine values of various angles in page 311, the value of inverse of given value is obtained as,

  ${\sin }^{-1}\left(0.1045\right)=6°$

f.

To determine

To calculate: the inverse cosine of a given value.

Answer to Problem 7CE

  ${\cos }^{-1}\left(0.1500\right)\simeq 81°$

Explanation of Solution

Given Information: The value 0.1500

Calculation:

Since the exact value if not directly found in the results in Page 311, using a scientific calculator, the value of inverse of given value is obtained as,

  $\begin{array}{c}{\cos }^{-1}\left(0.1500\right)=81.37°\\ \simeq 81°\end{array}$