Solved Examples on Sine Cosine Tangent Formula
Let’s solve some example questions on the Sin Cos Tan Values.
Example 1: The sides of the right-angled triangle are base = 3 cm, perpendicular = 4 cm, and hypotenuse = 5 cm. Find the value of sin θ, cos θ, and tan θ.
Solution:
Given that,
Base (B) = 3 cm,
Perpendicular (P)= 4 cm
hypotenuse (H) = 5 cm
From the trigonometric functions formula:
sinθ = P/H = 4/5
cosθ = B/H = 3/5
tanθ = P/H = 4/3
Example 2: The sides of the right-angled triangle are base = 3 cm, perpendicular = 4 cm, and hypotenuse = 5 cm. Find the value of cosecθ, secθ, and cotθ.
Solution:
Given that, Base(b) = 3 cm, Perpendicular (p)= 4 cm and hypotenuse(h) = 5 cm
From the trigonometric functions formula:
cosecθ = 1/sinθ = H / P = 5/4
secθ = 1/cosθ = H / B= 5/3
cotθ = 1/tanθ = B / P = 3/4
Example 3: Find θ if the base = √3 and perpendicular = 1 of a right-angled triangle.
Solution:
Since, the perpendicular and base of the right-angled triangle is given so tan θ is used.
tan θ = perpendicular/ base
tan θ = 1/√3
θ = tan-1(1/√3) [from trigonometric table]
θ = 30°
Example 4: Find θ if the base = √3 and hypotenuse = 2 of a right-angled triangle.
Solution:
Since the base and hypotenuse of the right-angled triangle are given so cosθ is used.
cos θ = base / hypotenuse
cos θ = √3/2
θ = cos-1(√3/2) [from trigonometric table]
= 30°
Sin Cos Tan Values
Sin, Cos, and Tan are the basic ratios of Trigonometry that are used to study the relationship between the angles and respective sides of a triangle. These ratios are initially defined on a Right Angled Triangle using Pythagoras Theorem.
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