SOLVING TRIGONOMETRIC EQUATIONS WORKSHEET

(1)  Find the principal solution and general solutions of the following:

(i)  sin θ = −1/√2

(ii) cot θ = √3

(iii) tan θ = -1/√3        Solution

(2)  Solve the following equations for which solutions lies in the interval 0° ≤ θ < 360°

(i) sin4 x = sin2 x          Solution

(ii) 2 cos2 x + 1 = −3 cos x      Solution

(iii) 2 sin2 x+1 = 3sinx            Solution

(iv) cos 2x  =  1 - 3 sin x        Solution

(3)  Solve the following equations:

(i) sin 5x − sin x = cos3x      Solution

(ii) 2 cos2 θ + 3sinθ − 3 = 0       Solution

(iii) cos θ + cos3θ = 2cos2θ      Solution

(iv) sin θ + sin3θ + sin5θ = 0        Solution

(v) sin 2θ − cos 2θ − sin θ + cos θ = 0      Solution

(vi)  sin θ + cos θ = 2      Solution

(vi)  sin θ + cos θ = √2             Solution

(vii) sin θ + √3 cos θ = 1       Solution

(viii) cot θ + cosecθ  = 3       Solution

(ix)  tan θ + tan (θ + π/3) + tan (θ + 2π/3)  =  √3     

 Solution

(x)  cos 2θ = (√5 + 1)/4       Solution

(xi)  2 cos2 x − 7 cos x + 3 = 0       Solution

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