Chapter 8, Problem 1P

(a)

To determine

To Find: The numerical and fractional values of the given angles in radian.

Answer to Problem 1P

Fractional value (in rad) = $\frac{\pi }{6}$ .

Numerical value (in rad) = $0.5235$ .

Explanation of Solution

Given:

Value of angle in degree, $30º$ .

Formula used:

  $\text{Radian=Degree}\times \frac{\pi }{180}$

Calculation:

Fractional value (in rad) = $30º\times \frac{\pi }{180}=\frac{\pi }{6}$ rad.

Using $\pi =3.141$

Numerical value (in rad) = $0.5235$ rad.

Conclusion:

The fractional and numerical values in radians are $\frac{\pi }{6}$ rad and $0.5235$ rad.

(b)

To determine

To Find: The numerical and fractional values of the given angles in radian.

Answer to Problem 1P

Fractional value (in rad) = $\frac{19\pi }{60}$ .

Numerical value (in rad) = $0.9946$ .

Explanation of Solution

Given:

Value of angle in degree, $57º$ .

Formula used:

  $\text{Radian=Degree}\times \frac{\pi }{180}$

Calculation:

Fractional value (in rad) = $57º\times \frac{\pi }{180}=\frac{19\pi }{60}$ rad.

Using $\pi =3.141$

Numerical value (in rad) = $0.9946$ rad.

Conclusion:

The fractional and numerical values in radians are $\frac{19\pi }{60}$ rad and $0.9946$ rad.

(c)

To determine

To Find: The numerical and fractional values of the given angles in radian.

Answer to Problem 1P

Fractional value (in rad) = $\frac{\pi }{2}$

Numerical value (in rad) = $1.5707$

Explanation of Solution

Given:

Value of angle in degree, $90º$

Formula used:

  $\text{Radian=Degree}\times \frac{\pi }{180}$

Calculation:

Fractional value (in rad) = $90º\times \frac{\pi }{180}=\frac{\pi }{2}$ rad.

Using $\pi =3.141$

Numerical value (in rad) = $1.5707$ rad.

Conclusion:

The fractional and numerical values in radians are $\frac{\pi }{2}$ rad and $1.5707$ rad.

(d)

To determine

To Find: The numerical and fractional values of the given angles in radian.

Answer to Problem 1P

Fractional value (in rad) = $2\pi$ .

Numerical value (in rad) = $6.283$ .

Explanation of Solution

Given:

Value of angle in degree, $360º$ .

Formula used:

  $\text{Radian=Degree}\times \frac{\pi }{180}$

Calculation:

Fractional value (in rad) = $360º\times \frac{\pi }{180}=2\pi$ rad.

Using $\pi =3.141$

Numerical value (in rad) = $6.283$ rad.

Conclusion:

The fractional and numerical values in radians are $2\pi$ rad and $6.283$ rad.

(e)

To determine

To Find: The numerical and fractional values of the given angles in radian.

Answer to Problem 1P

Fractional value (in rad) = $\frac{7\pi }{3}$ .

Numerical value (in rad) = $7.330$ .

Explanation of Solution

Given:

Value of angle in degree, $420º$ .

Formula used:

  $\text{Radian=Degree}\times \frac{\pi }{180}$

Calculation:

Fractional value (in rad) = $420º\times \frac{\pi }{180}=\frac{7\pi }{3}$ rad.

Using $\pi =3.141$

Numerical value (in rad) = $7.330$ rad.

Conclusion:

The fractional and numerical values in radians are $\frac{7\pi }{3}$ rad and $7.330$ rad.