Question

Find the degree measure corresponding to the following radian measures (Use π = 22/7)
(i) 9π/5 (ii) -5π/6 (iii) (18π/5)^c (iv) (-3)^c (v) 11^c (vi) 1^c

Answer 1

As we know that π rad = 180° ⇒ 1 rad = 180°/ π

(i)  9π/5 

[(180/π) × (9π/5)] ^o
By substituting the value of π = 22/7

[180/22 × 7 × 9 × 22/(7×5)]

(36 × 9) °

324°

Thus, degree measure of 9π/5 is 324°

(ii) -5π/6 

[(180/π) × (-5π/6)] ^o
By substituting the value of π = 22/7

[180/22 × 7 × -5 × 22/(7×6) ]

(30 × -5) °

– (150) °

∴ Degree measure of -5π/6 is -150°

(iii) (18π/5)^c

[(180/π) × (18π/5)] ^o
By substituting the value of π = 22/7

[180/22 × 7 × 18 × 22/(7×5)]

(36 × 18) °

648°

∴ Degree measure of 18π/5 is 648°

(iv) (-3)^c 

[(180/π) × (-3)] ^o

By substituting the value of π = 22/7

[180/22 × 7 × -3] ^o

(-3780/22) ^o

(-171 18/22) ^o

(-171 ^o (18/22 × 60)’)

(-171^o (49 1/11)’)

(-171^o 49′ (1/11 × 60)’)

– (171° 49′ 5.45”)

≈ – (171° 49′ 5”)

∴ Degree measure of (-3) ^c is -171° 49′ 5”

(v) 11^c

(180/ π × 11) ^o
By substituting the value of π = 22/7

(180/22 × 7 × 11) ^o

(90 × 7) °

630°

∴ Degree measure of 11^c is 630°

(vi) 1^c

(180/ π × 1) ^o

By substituting the value of π = 22/7

(180/22 × 7 × 1) ^o

(1260/22) ^o

(57 3/11) ^o

(57^o (3/11 × 60)’)

(57^o (16 4/11)’)

(57^o 16′ (4/11 × 60)’)

(57^o 16′ 21.81”)

≈ (57^o 16′ 21”)

Thus, degree measure of 1^c is 57^o 16′ 21”