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Trigonometric Identities – High School Level (Very Easy Explanation)

PURPOSE:

This document is prepared for high school students who find trigonometry difficult.

It explains trigonometric identities from ZERO level, with very simple language and step-by-
step solved examples.



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1. WHAT IS TRIGONOMETRY?



Trigonometry studies the relationship between angles and sides of a right-angled triangle.

If the angle changes, the side lengths also change. Trigonometry explains this change using
ratios.



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2. SIDES OF A RIGHT-ANGLED TRIANGLE



There are three sides:



1. Hypotenuse:

- The longest side

- Opposite the right angle

- Never changes position



2. Opposite:

- The side opposite to the chosen angle

, 3. Adjacent:

- The side next to the chosen angle



Note:

Opposite and adjacent change depending on the angle.

Hypotenuse never changes.



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3. BASIC TRIGONOMETRIC RATIOS



sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

tanθ = opposite / adjacent



Memory Trick:

SOH – CAH – TOA



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4. WHAT IS AN IDENTITY?



An identity is an equation that is always true for all values of the angle.

It does not depend on numbers.



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5. MOST IMPORTANT TRIGONOMETRIC IDENTITIES