Introduction to Trigonometry - Quick Look Revision Guide
Your 1-page summary of the most exam-relevant takeaways from Mathematic.
This compact guide covers 20 must-know concepts from Introduction to Trigonometry aligned with Class 10 preparation for Mathematics. Ideal for last-minute revision or daily review.
Complete study summary
Essential formulas, key terms, and important concepts for quick reference and revision.
Key Points
Definition of Trigonometry
Trigonometry studies relationships between sides and angles of triangles, essential for geometry.
Trigonometric Ratios
Defined for acute angles in right triangles: sin, cos, tan, cosec, sec, cot show side relationships.
Sine (sin A)
sin A = opposite/hypotenuse. Example: For angle A, if opposite is 3, hypotenuse is 5, sin A = 3/5.
Cosine (cos A)
cos A = adjacent/hypotenuse. If angle A has adjacent of 4 and hypotenuse of 5, cos A = 4/5.
Tangent (tan A)
tan A = opposite/adjacent. Example: For angle A with opposite 3 and adjacent 4, tan A = 3/4.
Reciprocal Ratios
Cosec A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A. Important for solving trigonometric equations.
Pythagorean Identity
sin²A + cos²A = 1 holds true for all angles, fundamental in simplifying expressions.
Values for Specific Angles
Key angles: sin 0° = 0, cos 0° = 1; sin 30° = 1/2, cos 30° = √3/2; sin 45° = cos 45° = 1/√2.
Angle Complements
For acute angles, sin A = cos(90° - A). Useful for deriving other ratios from known values.
Properties of Right Triangle
In a right triangle, the hypotenuse is the longest side, influencing the range of trigonometric values.
Examining Proportions
If tan A = 3/4, then in triangle ABC, opposite = 3k, adjacent = 4k for any k, aiding problem scaling.
Trigonometric Identity Proofs
sin²A + cos²A = 1 can be proved using the definitions of sine and cosine in a right-angled triangle.
Angle Addition Formula
sin(A + B) = sin A cos B + cos A sin B, handy for finding sine of combined angles.
Angle Subtraction Formula
sin(A - B) = sin A cos B - cos A sin B, important for complex angle calculations.
Applications of Trigonometry
Used in navigation, engineering, and physics for calculating distances and angles indirectly.
Striking Misconception
sin A and sin⁻¹ A are not the same; sin A is the ratio, while sin⁻¹ A is the inverse function.
Identifying Angles via Sine
If sin B = sin Q in two triangles, then ∠B = ∠Q for acute angles; deducing angle identities.
Use of Right Triangle Similarity
Similar triangles maintain the same angle ratios. If angle relationships are preserved, so are trigonometric ratios.
Understanding Cotangent
cot A = 1/tan A is essential for converting between ratios; helps in simplifying expressions.
Unit Circle Insights
Trigonometric functions correspond to points on a unit circle, providing geometric interpretations.
