Find the degree measure corresponding to the following radian measures (Use π = 22/7) ​

Question

Find the degree measure corresponding to the following radian measures (Use π = \(\frac{22}7\))

(i) \(\frac{9π}5\)

(ii) \(-\frac{5π}6\)

(iii) \((\frac{18π}5)^c\)

(iv) (-3)^c

(v) 11^c

(vi) 1^c

Answer 1

We know that π rad = 180° ⇒ 1 rad = 180°/ π

(i) Given \(\frac{9π}5\)

= \((\frac{180}π\times\frac{9π}5)^°\)

= (36 × 9) ° 

= 324°

(ii) Given \(-\frac{5π}6\)

=  \((\frac{180}π\times-\frac{5π}6)^°\)

= (30 × - 5) ° 

= - (150) °

(iii) Given \((\frac{18π}5)^c\)

= \((\frac{180}π\times\frac{18π}5)^°\)

= (36 × 18) ° 

= 648°

(iv) Given (-3)^c

= \((\frac{180}π\times-3)^°\)

= \((\frac{180}{22}\times7\times-3)^°\)

= \((-\frac{3780}{22})^°\)

= \((-171\frac{18}{22})°\)

= \((-171°(\frac{18}{22}\times{60})')\)

= \((-171°(49\frac{1}{11})')\)

= \((-171°{49}'(\frac{1}{11}\times60)')\)

= -(171° 49’ 5.45”) 

≈ -(171° 49’ 5”) 

(v) Given 11^c

^{= \((\frac{180}π\times11)^°\)}

= \((\frac{180}{22}\times7\times11)^°\)

= (90 × 7) ° 

= 630° 

(vi) Given 1^c

^{= \((\frac{180}π\times1)^°\)}

= ^{\((\frac{180}{22}\times7\times1)^°\)}

= \((\frac{1260}{22})^°\)

= \(({57}\frac{3}{11})^°\)

= \(({57}°(\frac{3}{11}\times{60})')\)

= \(({57}°({16}\frac{4}{11})')\)

= \((57°16'(\frac{4}{11}\times60)')\)

= (57° 16’ 21.81”) 

≈ (57° 16’ 22”)