The cosine formula, also known as the law of cosines, is a fundamental concept in trigonometry. It links the lengths of the sides of a triangle to the cosine of one of its angles.
Understanding the Cosine Formula - Testbook
Last Updated on Oct 08, 2024
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The Cosine Formula
The cosine formula is expressed as:
cos θ = A d j a c e n t/ H y p o t e n u s e
- a 2 = b 2 + c 2 − 2 b c . cos A
- b 2 = a 2 + c 2 − 2 a c . cos B
- c 2 = a 2 + b 2 − 2 a b . cos C
Examples to Understand Better
Example 1: Find the cosine of an angle in a right triangle with an adjacent side of 14 cm and a hypotenuse of 18 cm.
Solution:
Given:
Adjacent side = 14 cm
Hypotenuse = 18 cm c o s θ = A d j a c e n t/ H y p o t e n u s e
c o s θ = 14 c m/ 18 c m
c o s θ = 0.77
Examples to Understand Better
Example 1: Find the cosine of an angle in a right triangle with an adjacent side of 14 cm and a hypotenuse of 18 cm.
Solution:
Solution:
Given:
Adjacent side = 14 cm
Hypotenuse = 18 cm c o s θ = A d j a c e n t/ H y p o t e n u s e
Hypotenuse = 18 cm c o s θ = A d j a c e n t/ H y p o t e n u s e
c o s θ = 14 c m/ 18 c m
c o s θ = 0.77
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Frequently Asked Questions
What is the Cosine Formula?
In trigonometry, the law of cosines is also known as the cosine formula or cosine rule, relates the lengths of the sides of a triangle to the cosine of one of its angles.
What is the formula for Cosine?
The Cosine Formula is, cos θ = Adjacent/Hypotenuse.
How to calculate the cosine angle of a right triangle?
To calculate the cosine angle of a right triangle, you can use the formula cos θ = Adjacent/Hypotenuse. For example, if the adjacent side is 12 cm and the hypotenuse is 15 cm, then cos θ = 12/15 = 0.8.
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