Here's a very quick outline of what's been introduced in this tutorial :
Example: Consider the equation :
We solve it to get:
sin x = sin y
cos x =cos y
tan x = tan y
For solving these equations, we need to be familiar with the solutions of equations:
sin x=0, cos x=0, cot x=0.
sin x=sin y
=>sin x-sin y=0
=>sin (x-y)/2=0 or cos(x+y)/2=0
=>x-y=2nπ or x+y=(2m+1)π, m, nεZ
=>x=2nπ+y or x=(2m+1)π
=>x=(even multiple of π)+y or (odd multiple of π)-y
The solutions of cosec x= cosec y are also the same.
cos x= cos y
Following the similar procedure, we get
-2sin(x+y)/2 sin (x-y)/2=0.
=>x+y=2nπ or x-y=2mπ
sec x=sec y has the same solution.
tan x=tan y
=>sin x cos y=sinycosx
=>x=nπ+y , nεZ
cot x=cot y has the same solution
Here are the kind of questions which have been solved in this tutorial :
Solve sec x = 0.25.
Solve sin5x=0; x is in the range of 0 to π
Solve sin x+ sin 3x+sin 5x=0
Solve sin nx +cos mx=0.
Solve sin3x+cos2x=0Solve cot2x+3/sinx+3=0
Solve sin2x=sin2y, and tan2x=tan2y
Solve for general x, y sin (x – y) = 2 sin x sin y, where x and y are two acute angles of right angle triangle.
Solve the equation sin4 x + cos4 x = 7/2 sinx cosx
Companion MCQ Quiz for Trigonometric Equations (Basic Problems) - test how much you know about the topic ! Your score will be e-mailed to you at the address you provide.
Companion MCQ Quiz for Trigonometric Equations (More Challenging Problems) - test how much you know about the topic ! Your score will be e-mailed to you at the address you provide.