Trigonometry Angles

 The trigonometry angles which are commonly used in trigonometry problems are  0°, 30°, 45°, 60° and 90°. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. We will also show the table where all the ratios and their respective angle’s values are mentioned. To find these angles we have to draw a right-angled triangle, in which one of the acute angles will be the corresponding trigonometry angle. These angles will be defined with respect to the ratio associated with it.

For example, in a right-angled triangle,

Sin θ = Perpendicular/Hypotenuse

or θ = sin-1 (P/H)

Similarly,

θ = cos-1 (Base/Hypotenuse)

θ = tan-1 (Perpendicular/Base)

Trigonometry Table

Check the table for common angles which are used to solve many trigonometric problems involving trigonometric ratios.

Angles	0°	30°	45°	60°	90°
Sin θ	0	½	1/√2	√3/2	1
Cos θ	1	√3/2	1/√2	½	0
Tan θ	0	1/√3	1	√3	∞
Cosec θ	∞	2	√2	2/√3	1
Sec θ	1	2/√3	√2	2	∞
Cot θ	∞	√3	1	1/√3	0

In the same way, we can find the trigonometric ratio values for angles beyond 90 degrees, such as 180°, 270° and 360°.

Unit Circle

The concept of unit circle helps us to measure the angles of cos, sin and tan directly since the centre of the circle is located at the origin and radius is 1. Consider theta be an angle then,

Suppose the length of the perpendicular is y and of base is x. The length of the hypotenuse is equal to the radius of the unit circle, which is 1. Therefore, we can write the trigonometry ratios as;

Sin θ	y/1 = y
Cos θ	x/1 = x
Tan θ	y/x