Trigonometry Basics

5 min

Master ratios, standard angles, and core identities for SSC & Defence exams

Golden Rule

Trigonometry connects the sides and angles of a right-angled triangle. Master the basic ratios and fundamental identity sin²θ + cos²θ = 1 to solve complex questions quickly in SSC and Railway exams.

Exam Value

2 to 3 direct questions appear in every SSC CGL and CHSL tier.
Standard angle values save crucial time in height and distance problems.
Complementary angle rules help simplify large expression values instantly.

Memory Hooks

Use 'Pandit Badri Prasad Har Har Bole' for Sin, Cos, Tan ratios.
For sin values 0 to 90: write 0, 1, 2, 3, 4 under roots divided by 2.
Sin and Cos interchange at 90 minus theta for complementary angles.

Standard Angles

Ratio	0°	30°	45°
Sin θ	0	1/2	1/√2
Cos θ	1	√3/2	1/√2
Tan θ	0	1/√3	1

Visual Insights

Sin = P/H

(Perpendicular / Hypotenuse)

Perpendicular / Hypotenuse

Opposite side divided by longest side.

Cos = B/H

(Base / Hypotenuse)

Base / Hypotenuse

Adjacent side divided by hypotenuse.

Tan = P/B

(Perpendicular / Base)

Perpendicular / Base

Ratio of opposite to adjacent side.

Identity

(Sin² + Cos² = 1)

Sin² + Cos² = 1

True for any acute angle theta.

Exam Traps

sin²θ + cosθ = 1sin²θ + cos²θ = 1

Both trigonometric terms must be squared for the identity to equal 1.

sin(A+B) = sinA + sinBsin(A+B) = sinAcosB + cosAsinB

Never distribute sine across brackets directly. Use expansion formulas.

tan 0° = undefinedtan 0° = 0

Tan zero is zero because sin 0 is zero divided by cos 0 which is one.

Quick Test

Q1.If sin θ = 3/5, what is the value of cos θ in a right-angled triangle?

Q2.What is the value of sin 30° × cos 60° + cos 30° × sin 60°?

Page 27 of 35