Trigonometry identity questions are usually you are given an equation and you have to change either left or right side in to another, using the properties below.
| sin θ | = | 1 csc θ |
csc θ | = | 1 sin θ |
|
| cos θ | = | 1 sec θ |
sec θ | = | 1 cos θ |
|
| tan θ | = | 1 cot θ |
cot θ | = | 1 tan θ |
|
| tan θ = | sin θ cos θ |
cot θ = | cos θ sin θ |
|
sin²θ + cos²θ |
= | 1 | |
|
sin ( A+ β) |
= | sin A cos β + cos A sin β |
|
sin ( A− β) |
= | sin A cos β − cos A sin β |
|
cos ( A+ β) |
= | cos A cos β − sin A sin β |
|
cos ( A− β) |
= | cos A cos β + sin A sin β |
Most of the trig identity questions can be solved using these properties.
To prove a trig identity, you need to change one of the sides. The tip to solve trig identities is to pick more complicated looking side, and change it into a simpler side.
First step of the transforming a trig identity is to change all of the terms in sine and cosine. As tangent, secant, cosecant, cotangent all of the terms can be changed into terms sine and cosine.
Second step is to use property sin²θ+ cos²θ =1 to simply the equations.
Third step is to arrange the terms into the other side.
Example:
sin y+sin y cot^2y=csc y
Pick left side since it is more complicated one.
First step is to change cot into sine and cosine.
Siny + siny(cosy/siny)^2
= Siny + cos^2y / siny
= (sin^2y + cos^2y)/ siny
Since sin^2y + cos^2y = 1 apply this equation
= 1/siny
Now arrange this in terms of csc y
1/siny = csc y
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This article was written for you by Edmond, one of the tutors with Test Prep Academy.