Trigonometry Values Ratios Tables and Formulas

Trigonometry values of different ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant, deal with the measurement of lengths and angles of the right-angle triangle. The values of trigonometric functions for 0°, 30°, 45°, 60° and 90° are commonly used to solve trigonometry problems.

Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios. The word ‘trigon’ means triangle and ‘metron’ means ‘measurement’. It’s one of the major concepts and part of geometry, where the relationship between angles and sides of a triangle is explained.

Maths is an important subject, where we learn about different types of calculations and logic applied in our day-to-day life. Trigonometry basics are widely explained in students’ academic classes 9 and 10. Here, you will learn about different trigonometric ratios and formulas. Also, solve problems based on these formulas and identities to understand the fundamentals of trigonometry in a better way.Trigonometry Values Table

Let us learn, trigonometry values for angles  0°, 30°, 45°, 60° and 90°, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.

900Sin θ01/21/√2√3/21Cos θ1√3/21/√21/20Tan θ01/√31√3∞Cot θ∞√311/√30Sec θ12/√3√22∞Cosec θ∞2√22/√31

Suppose ABC is a right-angled triangle, right-angled at B. This triangle has a hypotenuse AC, an adjacent side AB which is adjacent to  ∠θ and a perpendicular BC opposite to ∠θ.

Trigonometry values are based on three major trigonometric ratios, Sine, Cosine, and Tangent.Sine or sin θ = Side opposite to θ / Hypotenuse = BC / ACCosines or cos θ = Adjacent side to θ / Hypotenuse = AB / ACTangent or tan θ =Side opposite to θ / Adjacent side to θ = BC / AB

Similarly, we can write the trigonometric values for Reciprocal properties, Sec, Cosec and Cot ratios.Sec θ = 1/Cos θ = Hypotenuse / Adjacent side to angle θ = AC / ABCosec θ = 1/Sin θ = Hypotenuse / Side opposite to angle θ = AC / BCCot θ = 1/tan θ = Adjacent side to angle θ / Side opposite to angle θ = AB / BC

Also,Sec θ . Cos θ =1Cosec θ . Sin θ =1Cot θ . Tan θ =1Trigonometry Ratios FormulaTan θ = sin θ/cos θCot θ = cos θ/sin θSin θ = 1/cosec θCos θ = sin θ/tan θ = 1/sec θSec θ = tan θ/sin θ = 1/cos θCosec θ = 1/sin θ

Also,Sin (90°-θ) = Cos θCos (90°-θ) = Sin θTan (90°-θ) = Cot θCot (90°-θ) = Tan θSec (90°-θ) = Cosec θCosec (90°-θ) = Sec θVideo Lesson on Trigonometry

Find the value of sin(90 – 45)°.

sin(90 – 45)° = cos 45° = 1/√2

If tan θ = 4 and sin θ = 6. Then find the value of cos θ.

We know, cos θ =  sin θ/ tan θ

Therefore, cos θ = 6/4 = 3/2Practice ProblemsFind the value of cos 30° + sin 60° cos 45°.What is the value of cos(90° + 60°) – tan 45°?Estimate the value of the expression: sec 45° cosec 60° + cot 30°

Keep learning Maths with us and download BYJU’S- The learning App, for interactive videos.Frequently Asked Questions – FAQsWhat is the value of sin 60 degrees?

The value of sin 60 degrees is given by:sin 60° = √3/2Is the value of sin 45 degrees 1/2?

No, the value of sin 45° is not equal to 1/2, but its value is 1/√2.Write the values of sin 30° and cos 60°.

The values of sin 30° and cos 60° are:sin 30° = 1/2cos 60° = 1/2How do you find the value of tan 45°?

tan 45° = sin 45°/cos 45°= (1/√2)/ (1/√2)= 1Therefore, the value of tan 45° = 1.