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Trigonometric Identities and Equations, Page 26

Trigonometric Equations: ExamplesCalculator on top of a notepad

Let’s go through some examples of solving trigonometric equations.

Example 1:

Solve sin x cot x = sqrt(3)/2 , for 0 degrees is less than or equal to x is less than 90 degrees.

sin x (cos x/sin x) = sqrt(3)/2; cos x = sqrt(3)/2; x = arccos(sqrt(3)/2); x = 30 degrees

Example 2:

Solve 2sin 3x = 1, for 0 is less than or equal to x is less than 2pi.

sin 3x = 1/2; 3x = arcsin 1/2; 3x = pi/6; x = pi/18

Example 3:

Solve csc2x - 2 = 0, for 0 degrees is less than or equal to x is less than 360 degrees.

(csc x)^2 = 2; csc x = ± sqrt(2); sin x = ± 1/sqrt(2) = ± sqrt(2)/2

x = 45°, 135°­, 225°, and 315°

Example 4:

Solve 2sin2x - 3sin x + 1 = 0, for 0 is less than or equal to x is less than 2pi. 

(2sin x - 1)(sin x - 1) = 0; 2sin x - 1 = 0 and sin x - 1 = 0; 2sin x - 1 = 0; 2sin x = 1; sin x = 1/2; x = pi/6, 5pi/6; sin x - 1 = 0; sin x = 1; x = pi/2, pi/6, 5pi/6