Trigonometry is the branch of algebra II. Algebra trigonometry deals with all of the trigonometric ratios and these trigonometric ratios are very much useful when you are dealing with the triangles and the unit circles. There are three main trigonometric ratios which exist in trigonometry and they are sin, cos and tan. The other three ratios are the reciprocal of the main ratios which are csc, sec and cot. They are outlined below: -
Cot x = 1/ tanx
Sec x = 1/cos x
Csc x = 1/ sinx
There are few basic angle values that is needed to be remembered, they are 0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees.
We have various trigonometric identities that are required to solve many of the trigonometric equations. We can see many examples of trigonometry in our day to day life.
Following are the few examples which are based on the algebra trigonometry.
Example 1: Find the value of tan 225 degrees.
Solution : Given: - tan 225 degrees
= tan (180 + 45) degrees
= tan 45 degrees
Hence the value of tan 225 degrees is 1.
Example: Prove that (sinx + cosx)^2 = 1 + sin 2x
Solution : - Given the left hand side as (sinx + cosx)^2
After expanding, we get
sin^2 x + cos^2 x + 2sinx cos x
= 1 + 2 sinx cosx [ sin^2 x + cos ^2 x = 1]
= 1 + sin 2x [sin 2x = 2 sin x cos x]