Trigonometric Functions

Trigonometric Functions

Board: CBSE | Class: Class 11

Comprehensive study notes for Trigonometric Functions by Ajay Yadav (Math King of Katargam). Master every concept with clear explanations, solved examples, and practice problems.

Key Concepts

Angle Measurement

Angle can be measured in degrees (1 revolution = 360°) or radians (1 revolution = 2π rad). π rad = 180°. 1 rad = 180°/π.

Trigonometric Ratios of Any Angle

For angle θ in standard position: sinθ = y/r, cosθ = x/r, tanθ = y/x, where (x,y) is a point on the terminal side and r = √x²+y².

Compound Angles

sin(A±B) = sinAcosB ± cosAsinB. cos(A±B) = cosAcosB −/+ sinAsinB. tan(A±B) = (tanA ± tanB)/(1 −/+ tanAtanB).

Multiple and Half Angles

sin2A = 2sinAcosA. cos2A = cos²A – sin²A = 1-2sin²A = 2cos²A-1. sin3A = 3sinA-4sin³A. cos3A = 4cos³A-3cosA.

Sum-to-Product Formulas

sinA+sinB = 2sin((A+B)/2)cos((A-B)/2). sinA-sinB = 2cos((A+B)/2)sin((A-B)/2). cosA+cosB = 2cos((A+B)/2)cos((A-B)/2). cosA-cosB = -2sin((A+B)/2)sin((A-B)/2).

General Solutions

sinθ = sinα ⇒ θ = nπ + (-1)ⁿα. cosθ = cosα ⇒ θ = 2nπ ± α. tanθ = tanα ⇒ θ = nπ + α.

Important Formulas

sin(A+B)sinAcosB + cosAsinB
cos(A+B)cosAcosB - sinAsinB
tan(A+B)(tanA+tanB)/(1-tanAtanB)
sin2A2sinAcosA
cos2Acos²A - sin²A = 2cos²A-1 = 1-2sin²A
Sum to ProductsinA+sinB = 2sin((A+B)/2)cos((A-B)/2)

Solved Examples

Example 1: Find sin15°.

Solution: sin15 = sin(45-30) = sin45cos30 – cos45sin30 = (1/√2)(√3/2) – (1/√2)(1/2) = (√3-1)/(2√2).

Example 2: Find general solution of sinθ = 1/2.

Solution: sinθ = sin30° = π/6. θ = nπ + (-1)ⁿ(π/6).

Example 3: Prove: sin3A = 3sinA – 4sin³A.

Solution: sin3A = sin(2A+A) = sin2AcosA + cos2AsinA = 2sinAcos²A + (1-2sin²A)sinA = 2sinA(1-sin²A) + sinA – 2sin³A = 3sinA – 4sin³A.

Practice Questions

  1. Find cos75°.
  2. If sinA = 3/5 and cosB = 5/13, find sin(A+B).
  3. Solve: 2cos²θ – 3cosθ + 1 = 0.
  4. Prove: cosAcos2Acos4A…cos2ⁿ⁻¹A = sin(2ⁿA)/(2ⁿsinA).
  5. Find general solution of tanθ = √3.

Download PDF

Click here to download the PDF notes.

Video Lessons

Watch video explanations on our Videos page.

Scroll to Top