Maths F.5 Trigonometry

1) Solve cos(150° + x) = sin120° where x is larger than orequal to 0 and is smaller than or equal to 180°.

Solution :
0° ≤ x ≤ 180°
150° ≤ (150° + x) ≤ 330°

cos(150° + x) = sin120°
cos(150° + x) = sin(180° - 120°)
cos(150° + x) = sin60°
cos(150° + x) = cos(90° - 60°)
cos(150° + x) = cos30°
cos(150° + x) = cos(360° - 30°)
cos(150° + x) = cos330°
150° + x = 330°
x = 180°


2) Solve the equation (sinx)² - sinx cosx = 6(cosx)² for x is larger than orequal to 0° and is smaller than 360°. (corr the answer to 1 d.p.)

Solution :
(sinx)² - sinx cosx = 6(cosx)²
(sinx)² - sinx cosx - 6(cosx)² = 0
[(sinx)² - sinx cosx - 6(cosx)²] /(cosx)² =0
(tanx)² - tanx - 6 = 0
(tanx + 2)(tanx - 3) = 0
tanx = -2, 3
x = (180-63.4)°,(360-63.4)°,71.6°, (180+71.6)°
x = 116.6°, 296.6°,71.6°, 251.6°