Question #6a6d6

1 Answer
Jan 6, 2018

Qn 3 (a) x = 11.537^0, -30^0

Qn 3 (c) x = 30^0, 150^0, 90^0, -90^2

Qn 4 (a) a = 81, A = 43, b = 62, B = 31, c = 114.2, C = 106

Explanation:

Qn 3 (a)
10cos^2x+ 3sinx - 9 = 0

10 (1-sin^2x) + 3sinx - 9 = 0

-10sin^2x + 3sinx + 1 = 0

-10sin^2x - 5sinx + 2sinx + 1 = 0

-5sinx(2sinx +1) + 1(2sinx + 1) = 0

(1-5sinx)(2sinx+1) = 0

sinx = 1/5, -1/2)

x = 11.537^0, -30^0

Qn 3 (c)

2sin^3x - sin^2x - 2sinx + 1 = 0

sin^2x(2sinx -1) - 1(2sinx -1) = 0

(sin^2x-1)(2sinx-1) = 0

sin^2x = 1, sinx = +-1, x = 90^0, -90^0

2sinx = 1, x = 30^0, 150^0

Qn 4 (a)
Given A = 43^0, a = 81, b = 62

a / sin A = b / sin B = c / sin C

81 / sin 43 = 62 / sin B

sin B = (62/81) * sin 43 = 0.522

/_B = sin^-1 0.522 = 31.4665 ~~ 31^0

#/_C = 180 - /_A - /_B = 180 - 43 - 31 = 106^0$

81 / sin 43 = c / sin 106

c = (81*sin 106) / sin 43 = 114.1677 ~~114.2

.a = 81, A = 43, b = 62, B = 31, c = 114.2, C = 106