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Trigonometric Ratios of Complementary Angles

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We know that complementary angles are the set of two angles such that their sum is equal to 90°. For example: 30° and 60° are complementary to each other as their sum is equal to 90°.The triangle ∆ABC given below, is right angled at B; ∠A and ∠C form a complementary pair.

notes

Recall that two angles are said to be complementary if their sum equals 90°. In

ABC, right-angled at B.

Let ∠A= θ

In ∆ABC,

A+∠B+∠C= 180° (Angle sum property)

θ+ 90°+∠C= 180°

C= 180°-90°-θ

C= (90°-θ)

Trigonometric ratios-

1) sin(90°-θ)= `"AB"/"AC"`= cosθ

 

2) cos(90°-θ)= `"BC"/"AC"`= sinθ

 

3)tan(90°-θ)= `"AB"/"BC"`= cotθ

 

4)cot(90°-θ)= `"BC"/"AB"`= tanθ

 

5)sec(90°-θ)= `"AC"/"BC"`= cosecθ

 

6)cosec(90°-θ)= `"AC"/"AB"`= secθ

 

Example: Evaluate `"sin18°"/"cos72°"`

 

solutioin- `"sin(90°-72°)"/"cos72°"`

 

sin(90°-θ)= cosθ= `"cos72°"/"cos72°"= 1`

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Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Shaalaa.com | Trigonometric Identities part 1 (Ratio complementary angle)

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Trigonometric Identities part 1 (Ratio complementary angle) [00:10:14]
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