Category Archives: Trigonometric functions and equations

Trigonometric Equations 3

Solve 2 sin x – sin x cos x = 0 for
-π< x <π. 

Solution: -3π/4, 0, π/4

sin x( sin x – cos x ) = 0

sin x = 0        or      sin x – cos x = 0

sin x = 0                 sin x = cos x

x=0                         sin x/ cos x = 1            

                               tan x = 1

                               basic ∠, a = π/4

                               x is in the 1st or 3rd quadrant

                               x = π/4 or   x = -3π/4

Trigonometric Equations 2

Find all the angles between 0° and 360° which satisfy the equation sec y(1 + tan y) = 6 cosec y.

Solution: y= 63.4, 243.4, 108.4, 288.4

1/cosy (1 + tany) = 6(1/siny)

1 + tany = 6 cosy/siny

1 + tany = 6 coty

tany + tan2y = 6

tany + tan2y – 6 = 0

tany = 2                 or                tany = -3

1st and 3rd quadrant                2nd and 4th quadrant

y = 63.435, 243.43                    y= 108.43, 288.43

y = 63.4, 243.4                          y = 108.4, 288.4

Trigonometric Equations

Solve sinx – 0.5 = 0 such that -360° < x < 360°.

Solution: 30°, 150°, -330°, -210°

Basic angle, a = 30°

sinx = 1/2

x = angle 1 / 30° , angle 2/ (180° – 30°)

x =   30°, 150° 

     -360°  -360 °

x = -330°, -210°

x = 30°, 150°, -330°, -210°