Question

Find the degree measures corresponding to the following radian measures (Use π = 22/7).
(i) 11/16
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Answer 1

$radian \: measure = \frac{\pi}{180} \times degree \:$

$\frac{11}{16} = \frac{\pi}{180} \times degree \: measure$

$\frac{11}{16} \times \frac{180}{\pi} = degree \: measure$

$degree \: measure = \frac{11}{16} \times \frac{180}{22} \times 7$

$degree \: measure = \frac{11 + 180 \times 7}{16 \times 22}$

$= \frac{1 \times 90 \times 7}{8 \times 2} \\ \\ = \frac{1 \times 45 \times 7}{4 \times 2} \\ \\ = \frac{315}{8}$

By dividing this number ,we get 39 as quotient, 3 as remainder and 8 as divisor

So, we can right it as

$= 39 \degree + \frac{3 \degree}{8} \\ \\ = 39 \degree + ( \frac{3}{8} \times 60) \prime$

1° = 60

$= 39 \degree + ( \frac{45}{2} ) \prime$

$= 39 \degree + (22 \frac{1}{2} ) \prime$

$= 39 \degree + (22) \prime + ( \frac{1}{2} ) \prime$

$= 39 \degree + (22) \prime + ( \frac{1}{2} \times 60) \prime \prime$

$\because 1 \prime \: = 60 \prime \prime$

$degree \: measure = 39 \degree + (22) \prime + (30) \prime \prime$

$degree = 39 \degree \: 22 \prime \: 30 \prime \prime$

$\prime = minute \\ \prime \prime = seconds$

Answer 2

Answer:

11/16 radian = (11/16) (180°/π)  {as 180° = π radian, then 1 radian = 180°/π}

                              = (11/16) × (180° × 7/22)

                              = (11 × 180° × 7/16 × 22)

                             = 315/8°

                             = 39 (3/8)°

                            = 39(3/8)°

                            = 39° + (3/8)°

Again 1° = 60′

So (3/8)° = 60′ × (3/8)

                    = 22 (1/2)’

                    = 22 (1/2)’ 

                    = 22′ + 1/2′

Again 1′ = 60″

                   = (1/2)’ = 30″

So 39 (3/8)° = 39° 22′ 30″

Thank You Preetu ❤