๐Ÿ” Introduction

Trigonometry deals with relationships between the angles and sides of right-angled triangles. It's widely used in navigation, architecture, engineering, and physics.

๐Ÿ“ 1. Trigonometric Ratios

In a right triangle:

  • Hypotenuse = longest side

  • Opposite side = side opposite to the angle

  • Adjacent side = side next to the angle (not hypotenuse)

Let’s say ∠A is the angle in right triangle ABC:

RatioFormulaPronunciation
sin AOpposite / HypotenuseSine A
cos AAdjacent / HypotenuseCosine A
tan AOpposite / AdjacentTangent A
cot A1 / tan A = Adjacent / OppositeCotangent A
sec A1 / cos A = Hypotenuse / AdjacentSecant A
cosec A1 / sin A = Hypotenuse / OppositeCosecant A

๐Ÿ“ 2. Values of Trigonometric Ratios (Standard Angles)

ฮธ (degrees)sin ฮธcos ฮธtan ฮธ
0°010
30°1/2√3/21/√3
45°1/√21/√21
60°√3/21/2√3
90°10Not Defined

✅ Use the triangle trick (1, √3, 2) for quick recall.

๐Ÿ”„ 3. Trigonometric Identities

These identities are always true for any angle A (where defined):

  1. sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1

  2. 1+tan⁡2A=sec⁡2A1 + \tan^2 A = \sec^2 A

  3. 1+cot⁡2A=csc⁡2A1 + \cot^2 A = \csc^2 A

๐Ÿ” 4. Complementary Angles

Two angles are complementary if their sum is 90°.

sin(90° − A) = cos Atan(90° − A) = cot A
cos(90° − A) = sin Acot(90° − A) = tan A
sec(90° − A) = cosec Acosec(90° − A) = sec A

๐Ÿ’ก Key Points to Remember

  • Trigonometric ratios are always based on a right triangle.

  • Values of ratios at standard angles are important for MCQs.

  • Identities help simplify complex expressions.

  • Complementary angle formulas are common in exams.

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