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Trigonometric Functions

General solutions of some trigonometric equations: , where n ∈ Z ,where n ∈ Z sin x = sin y ⇒ x = nπ + (–1)n y, where n ∈ Z cos x = cos y ⇒ x = 2nπ ±y, where n ∈ Z tan x = tan y ⇒ x = nπ + y, where n ∈ Z

 

Example 1: Solve cot x cos2 x = 2 cot x 

Solution:

 

But this is not possible as –1 ≤ cos x ≤ 1

Thus, the solution of the given trigonometric equation is  where n ∈ Z.

 

Example 2: Solve sin 2x + sin 4x + sin 6x = 0.

Solution:

 

Thus, , where m, n ∈ Z

 

1. If A(x, y) is any point on the terminal arm OQ such that OA = r = and ∠POQ = q  then:

sin q =

cos q =  

tan q = , where x ≠ 0

cosec q = , where y ≠ 0

sec q = , where x ≠ 0

cot q = , where y ≠ 0

 

2. The signs of various trigonometric ratios in different quadrants are as follows:

Properties and Solutions of Triangles …

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