# Sin to Cos Formula

A triangle whose one angle is a right angle triangle is called a right-angled triangle. The longest side of this triangle is called the hypotenuse and it is always opposite to the angle which is 90 degrees. the side which is between the angle to be found and the right angle is called an adjacent side. The side opposite the angle to be found is called the opposite side.

• Sin x = length of opp side/length of hypotenuse = o / h
• Cosine x= the length of adjacent side/ the length of hypotenuse = a/h
• Tangent x = the length of opp side/ the length of the adjacent side = o/a
 Sin 2 x = 1 – Cos 2 x

## Examples of Sin to Cos formula

Example 1: Find the value of sin x , if cos x = â…˜?

Solution: Sin 2 x = 1 – Cos2 x

= 1 – ( â…˜)2

= 1 – 16/25

= (25 – 16) / 25

= 9 /25

sin x = 3/5

Example 2: If sin x = 5/13, then what is the value of cos x?

Solution:
Given,
sin x = 5/13
cos = âˆš(1 – sin2x)
= âˆš(1 – 25/169)
= âˆš(144/169)
= 12/13

Example 3: If sin A + sin2A = 1, then find the value of (cos2A + cos4A).

Solution:
Given,
sin A + sin2A = 1
sin A = 1 – sin2A
sin A = cos2A
Squaring on both the sides,
sin2A = cos4A
1 – cos2A = cos4A
Therefore, cos2A + cos4A = 1