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Sine Cosine Tangent Formula

To calculate the angle of a right triangle, sine cosine tangent formula is used. The ratio of the different sides of the triangle gives the sine, cosine, and tangent angles. Here, the hypotenuse is the longest side, the side opposite to the hypotenuse is the opposite side and the where both the sides rest is the adjacent side. A right angle looks like this:

Sine Cosine Tangent Formula

Formulas for Sine, Cos, Tan

The Sine Cosine Tangent Formula is,

Angle NameAngle Formula
Sine Angle FormulaSin θ = Opposite side ⁄Hypotenuse
Cos Angle FormulaCos θ = Adjacent side⁄Hypotenuse
Tangent Angle FormulaTan θ = Opposite Side ⁄Adjacent Side

Solved Examples

Question 1: Calculate the angle in a right triangle whose adjacent side and hypotenuse are 12 cm and 20 cm respectively? Solution:

Given,

Adjacent side = 12 cm

Hypotenuse = 20 cm

cos θ = Adjacent⁄Hypotenuse

cos θ = 12⁄20

θ = cos−1(0.6)

θ = 53.13

Question 2: If sin A = 21/29 and cos A = 20/ 29, then find the value of tan A.

Solution:
Given,
sin A = 21/29
cos A = 20/29
We know that,
sin θ = Opposite/Hypotenuse
cos θ = Adjacent/Hypotenuse
Thus,
Opposite = 21
Adjacent = 20
Hypotenuse = 29
Therefore, tan A = Opposite/Adjacent
= 21/20

Question 3: If sin A = ⅗, then find the value of cos A and tan A.

Solution:
Given,
sin A = Opposite/Adjacent = ⅗
By Pythagoras theorem,
(Hypotenuse)2 = (Opposite side)2 + (Adjacent side)2
52 = 32 + (Adjacent side)2
(Adjacent side)2 = 25 – 9 = 16
Adjacent side = √16 = 4
Therefore,
cos A = Adjacent/Hypotenuse = ⅘
tan A = Opposite/Adjacent = ¾