Trigonometry Values

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 ‘metry’ 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 student’s academic classes of 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 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 00, 300, 450, 600 and 900 are commonly used to solve trigonometry problems.

Let us know here the trigonometry values of sin, cos, tan functions for standard angles, along with table created for those values and trigonometric formulas in this article.

Values of Trigonometry Ratios

Let us learn, trigonometry values for angles  00, 300, 450, 60and 900, with respect to sin, cos, tan, cot, sec, cosec functions, taking an example of the right-angle triangle.

trigonometry values

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 sinθ = \(\frac{Side opposite to θ}{Hypotenuse}\)=\(\frac{BC}{AC}\)

Cosines or cosθ = \(\frac{Adjacent side to θ}{Hypotenuse}\)=\(\frac{AB}{AC}\)

Tangent or tanθ = \(\frac{Side opposite to θ}{Adjacent side to θ}\)=\(\frac{BC}{AB}\)

Similarly, we can write the trigonometric values for Reciprocal properties, Sec, Cosec and Cot ratios.

Secθ = 1/Cosθ = \(\frac{Hypotenuse}{Adjacent side to angleθ}\) = \(\frac{AC}{AB}\)

Cosecθ = 1/Sinθ = \(\frac{Hypotenuse}{Side opposite to angle θ}\) = \(\frac{AC}{BC}\)

Cotθ = 1/tanθ = \(\frac{Adjacent side to angle θ}{Side opposite to angleθ}\)=\(\frac{AB}{BC}\)

Also,

Secθ . Cosθ =1

Cosecθ . Sinθ =1

Cotθ . Tanθ =1

Trigonometry Table Based On Standard Angles

Based on trigonometric values for some standard angles, we have created a table to make students learn them easily and also use them while solving trigonometry problems.

Angle

00

300 450 600

900

Sin θ 0 1/2 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 1/2 0
Tan θ 0 1/√3 1 √3
Cot θ √3 1 1/√3 0
Sec θ 1 2/√3 √2 2
Cosec θ 2 √2 2/√3 1

We can also use below given formulas to find the values of trigonometry ratios;

  • Tan θ = sin θ/cos θ
  • Cot θ = cos θ/sin θ
  • Sin θ = tan θ/cos θ
  • Cos θ = sin θ/tan θ
  • Sec θ = tan θ/sin θ
  • Cosec θ = cos θ/tan θ

Also,

  • Sin (90-θ) = Cos θ
  • Cos (90-θ) = Sin θ
  • Tan (90-θ) = Cot θ
  • Cot (90-θ) = Tan θ
  • Sec (90-θ) = Cosec θ
  • Cosec (90-θ) = Sec θ

Trigonometry Examples

Problem: Find the value of sin(90-45)0.

Solution: sin(90-45)0 = cos 450 = 1/√2

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

Solution: We know, cosθ = \(\frac{sin\theta}{tan\theta }\)

Therefore, cosθ = 6/4 = 3/2

Keep learning Maths with us and download BYJU’S- The learning App, for interactive videos.


Practise This Question

In the below figure, ___ angles are present and they are ___