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Trigonometry

In a triangle, the ratio of the sides varies with the variation in the angle of the triangle. We can find the relationship between the angles and lengths of sides using trigonometry, a branch of mathematics which deals with the measurement of the angles and the sides of a triangle and of the various relationships existing between them.

Trigonometric Ratios

Let ABC be a right-angled triangle, right-angled at B with ACB = θ. With three sides of the triangle, we can have six different ratios (see Figure). These ratios are given different names. The following table gives the ratios, their names and the relationship between the ratios:

 


Figure. A Right-Angled Triangle

 

Ratio Sides

Name of the Trigonometric Ratio

Symbol

Description: 35889.png 

sine of θ

sin θ

Description: 35897.png 

cosine of θ

cos θ

Description: 35904.png 

tangent of θ

tan θ

Description: 35914.png 

cotangent of θ

cot θ

Description: 35924.png 

secant of θ

sec θ

Description: 35937.png 

cosecant of θ

cosec θ

 

Relationship between trigonometric ratios

  1. sin θ = Description: 35949.png
  2. cos θ = Description: 35959.png
  3. tan θ = Description: 35971.png

Trigonometric Ratios of Standard Angles

The following table gives the trigonometric ratios of standard angles.

Angle θ

Ratios

30°

45°

60°

90°

sin θ

0

Description: 35981.png

Description: 35993.png

Description: 36000.png

1

cos θ

1

Description: 36008.png

Description: 36015.png

1/2

0

tan θ

0

Description: 36023.png

1

Description: 36035.png

infinity





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