3.Trigonometrical Ratios, Functions and Identities
medium

Find the degree measures corresponding to the following radian measures (Use $\pi=\frac{22}{7}$ ).

$-4$

A

$-229^{\circ} 5^{\prime} 27^{\prime \prime}$

B

$-229^{\circ} 5^{\prime} 27^{\prime \prime}$

C

$-229^{\circ} 5^{\prime} 27^{\prime \prime}$

D

$-229^{\circ} 5^{\prime} 27^{\prime \prime}$

Solution

We know that $\pi$ radian $=180^{\circ}$

$-4$ radian $=\frac{180}{\pi} \times(-4)$ degree

$=\frac{180 \times 7(-4)}{22}$ degree

$=\frac{-2520}{11}$ degree $=-229 \frac{1}{11}$ degree

$=-229^{\circ}+\frac{1 \times 60}{11}$ minutes      $\left[1^{\circ}=60^{\prime}\right]$

$=-229^{\circ}+5^{\prime}+\frac{5}{11}$ minutes

$=-229^{\circ} 5^{\prime} 27^{\prime \prime} \quad\left[1^{\prime}=60^{\prime \prime}\right]$

Standard 11
Mathematics

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