Trigonometry Angles: Overview, Questions, Preparation

Trigonometry is defined as the study of angles and their functions, which also helps students understand how these functions can apply to calculations. The angles with which the trigonometric functions are expressed are known as trigonometry angles. These usually measure anywhere between 0°, 30°, 45°, 60° and 90° and are considered to be standard for trigonometric ratios, like sin, cos, tan and cosec. 

Trigonometry angles are those angles which are derived from the ratios of trigonometric functions. On the contrary, trigonometry as a subject deals with studying angles and their relationships with the triangles. The angle values here range between 0 and 360 degrees in total, with the aforementioned main trigonometric ratios, i.e., sin, cos, tan, sec and cosec. 

Trigonometric angles can be measured either in terms of degrees or radians, but the former is the most preferred unit of measurement. Given that a circle can be divided into 360 sub-parts, we can obtain a right angle with 90°. It must also be noted that a degree can further be divided into 60 minutes and then 60 seconds, which are represented by symbols such as °’,’ and “. 

On the other hand, radian is also used to measure angles and a circle with a radian 1 can determine an arc with a length of the radius. Since the length of a full circle is 2πr, you can say that a circle contains 2πr. 

 In order to simplify the process of calculating trigonometric numbers at various angles, we can use reference angles which have been derived from different trigonometric functions. A trigonometric table is given below to define all values of trigonometric ratios - 

Formulas associated with trigonometry angles are based on 4 quadrants of a circle, as represented below - 

Supplementary Angles (Sum is equal to π) 

(sin π - X) = Sin X

(cos π - X) = cos X

(tan π - X) = tan X

(cot π - X) = cot 

Anti-Supplementary Angles (Difference is equal to π)

(sin π + A) = - sin A

(cos π + A) = - cos A

(tan π + A) = tan A

(cot π + A) = cot 

Opposite Angles (sum is 2πr)

sin (2π - A) = -sin A

cos (2π - A) = cos A

tan (2π - A) = -tan A

cot (2π - A) = -cot A

Complementary Angles (sum is π/2)

sin (π/2 - A) = sin A

cos (π/2 - A) = cos A

tan(π/2 - A) = tan A

cot (π/2 - A) = cot A

Importance and Weightage in Class 10th 

It is important to know about trigonometric angles in Class 10th in order to clear your basics & build upon your knowledge in subsequent classes. The topic is taught as part of the ‘Introduction to Trigonometry’ chapter and in terms of weightage, contributes around 12 marks to the overall question paper. 

Find the value of sin 90 - cos 60

Answer: sin 90 = 1

                cos 60 = ½ 

sin 90 - cos 60 = 1-½ = 0.5 

Evaluate 3cos 60+tan 45

Answer: cos 60 = ½; tan 45 = 1

3(½) + 1 = 3/2+1 = 5/2 

Find the value of cosec 30+tan 45

Answer: cosec 30 = 2

                tan 45= 1

cosec 30+tan 45 = 2+1 = 3

Q: What do you understand by allied angles in trigonometry?

Q: What are trigonometric ratios?

Q: What are trigonometry angles?

Q: What symbols are used to measure trigonometry angles?

Q: What are some properties of trigonometric angles?