What are Trigonometric Ratios?
Trigonometric ratios are ratios of the sides of a right-angled triangle with respect to a particular acute angle.
The value of a trigonometric ratio depends on the angle θ and the relationship between the sides of the triangle.
Always identify Perpendicular, Base and Hypotenuse with respect to angle θ before using any formula.
Find the three sides
Before using any formula, identify thePerpendicular,BaseandHypotenusewith respect to angle θ.
The three fundamental ratios
The three basic trigonometric ratios aresin θ,cos θandtan θ.
Sine of an angle is the ratio of Perpendicular to Hypotenuse.
Cosine of an angle is the ratio of Base to Hypotenuse.
Tangent of an angle is the ratio of Perpendicular to Base.
Remember SOH-CAH-TOA
A simple way to remember the three basic trigonometric ratios isSOH-CAH-TOA.
Test Your Understanding
Calculating Trigonometric Ratios
In a right triangle, Perpendicular = 6 cm, Base = 8 cm and Hypotenuse = 10 cm. Find sin θ, cos θ and tan θ.
Solution:
- sin θ = 6/10 = 3/5
- cos θ = 8/10 = 4/5
- tan θ = 6/8 = 3/4
Finding Ratios From sin A
If sin A = 3/5, find cos A and tan A.
Solution:
Let Perpendicular = 3k and Hypotenuse = 5k.
By Pythagoras theorem:
Base = √(25k² - 9k²) = 4k
tan A = 3/4
What did we learn?
Trigonometric ratios describe the relationship between sides of a right-angled triangle.
The three basic ratios aresin θ,cos θandtan θ.
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base