1 3 Trigonometric Equation Example 1 Solve the

1. 3 Trigonometric Equation Example 1 : Solve the following equations : (a) tan x = 0. 6234 for 0 o < x < 180 o (b) sin x = - 0. 5 for -90 o < x < 90 o (c) cos 2 x = 0. 5 for - 31. 9 o - 30 o <x< (d) sin ( 2 x – 60 o ) = – 0. 5 for - 180 o < x < 180 o - 165 o, - 450, 1350 (e) 2 tan 2 x = 3( 1 + sec x ) for 0 o < x < 360 o (f) 66. 4 o , 1800, 293. 6 o cos 3 x + cos x = cos 2 x for 0 o < x < 360 o Ex 1. 5 pg. 26 Q. 1 – 3 ( b , d ) , 4 – 7 45 o , 600, 135 o, 2250, 3000, 3150

1. 3 Trigonometric Equation Example 2 : Solve the following equation by giving your answer correct to the nearest 0. 1 o : (a) 5 tan y + sec y + 5 = 0 for 0 o < y < 360 o Half Angle Formulae When to use ? ? to solve the trigonometric equation which cannot be solved by using identities

Example 2 : Solve the equation 5 tan y + sec y + 5 = 0 for 0 o < y < 360 o using Solution : 5 tan y + sec y + 5 = 0 . . . y = 143. 10 or 306. 9 o When to use ? ? The equation cannot be solved by using identities Reduced the equation to an algebraic equation in terms of t

Example 3 : show that the trigonometric equation sin y + 2 cos y = 1 can be written in the form at 2 + bt + c = 0 , where a, b and c are constants. Hence, solve this equation for all angles between 0 o and 360 o Solution : sin y + 2 cos y = 1 . . . y = 90 o or 323. 2 o . Ex 1. 6 pg. 31 3 t 2 – 2 t – 1 = 0 Q. 1 – 4