Class 10 Maths - Trigonometry
Trigonometry deals with the relationship between sides and angles of a triangle.
1. Trigonometric Ratios (P-B-H)
Mnemonic: "Some People Have, Curly Black Hair, Through Proper Brushing"
- Sin $\theta = \frac{P}{H}$
- Cos $\theta = \frac{B}{H}$
- Tan $\theta = \frac{P}{B}$
(Reciprocals: Cosec, Sec, Cot)
2. The Table (Values)
| Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| Sin | 0 | $\frac{1}{2}$ | $\frac{1}{\sqrt{2}}$ | $\frac{\sqrt{3}}{2}$ | 1 |
| Cos | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{1}{\sqrt{2}}$ | $\frac{1}{2}$ | 0 |
| Tan | 0 | $\frac{1}{\sqrt{3}}$ | 1 | $\sqrt{3}$ | $\infty$ |
3. Pythagorean Identities
- $\sin^2 \theta + \cos^2 \theta = 1$
- $1 + \tan^2 \theta = \sec^2 \theta$
- $1 + \cot^2 \theta = \text{cosec}^2 \theta$
4. Complementary Angles & Heights and Distances
- $\sin(90 - \theta) = \cos \theta$
- Angle of Elevation: Looking up.
- Angle of Depression: Looking down.
Practice Proof questions daily! "LHS = RHS" is the goal. 📐📏
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