| --- |
| source: ncert |
| topic: trigonometry |
| class_level: class_10 |
| chapter: ch8 |
| difficulty: intermediate |
| --- |
| |
| Class 10 | Ch8: Introduction to Trigonometry |
| TRIGONOMETRIC RATIOS (right triangle, angle theta): |
| sin(theta)=opposite/hypotenuse=P/H. |
| cos(theta)=adjacent/hypotenuse=B/H. |
| tan(theta)=opposite/adjacent=P/B=sin/cos. |
| cosec(theta)=1/sin=H/P. sec(theta)=1/cos=H/B. cot(theta)=1/tan=B/P. |
| STANDARD VALUES TABLE: |
| Angle: 0° 30° 45° 60° 90° |
| sin: 0 1/2 1/sqrt2 sqrt3/2 1 |
| cos: 1 sqrt3/2 1/sqrt2 1/2 0 |
| tan: 0 1/sqrt3 1 sqrt3 undefined |
| cosec: undef 2 sqrt2 2/sqrt3 1 |
| sec: 1 2/sqrt3 sqrt2 2 undef |
| cot: undef sqrt3 1 1/sqrt3 0 |
| TRIGONOMETRIC IDENTITIES: |
| sin^2(theta)+cos^2(theta)=1. |
| 1+tan^2(theta)=sec^2(theta). |
| 1+cot^2(theta)=cosec^2(theta). |
| COMPLEMENTARY ANGLES: |
| sin(90-A)=cos(A). cos(90-A)=sin(A). tan(90-A)=cot(A). |
| cosec(90-A)=sec(A). sec(90-A)=cosec(A). cot(90-A)=tan(A). |
| SOLVED EXAMPLES: |
| Example 1: If sin(theta)=3/5, find all trig ratios. |
| P=3, H=5, B=sqrt(25-9)=4. |
| cos=4/5, tan=3/4, cosec=5/3, sec=5/4, cot=4/3. |
| Example 2: Prove (sin^2(theta)/cos(theta)) + cos(theta) = sec(theta). |
| LHS=sin^2/cos+cos=(sin^2+cos^2)/cos=1/cos=sec. Proved. |
| Example 3: Evaluate 2tan^2(45°)+cos^2(30°)-sin^2(60°). |
| =2(1)^2+(sqrt3/2)^2-(sqrt3/2)^2=2+3/4-3/4=2. |
| Example 4: sin(theta)=cos(theta). Find theta. |
| tan(theta)=1. theta=45°. |
| COMMON MISTAKES: |
| sin^2+cos^2=1 (NOT sin+cos=1). |
| Values at 90°: sin=1, cos=0, tan=undefined (NOT 0). |
| Memorise table using: "Some People Have Curly Brown Hair Through Proper Brushing". |
