U2 Trigonometry(KA/PRE/U2)

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Unit 2: Trigonometry

Special Trigonometric Values in the First Quadrant

In the first quadrant (0° to 90°), sine, cosine, and tangent are all positive. Key angles: 30°, 45°, 60°.

Trigonometric Identities on the Unit Circle

The unit circle shows that sin²θ + cos²θ = 1 for all angles θ.

Inverse Trigonometric Functions

Inverse functions (like sin⁻¹x) return angles based on given trigonometric ratios.

Law of Sines & Law of Cosines

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines: c² = a² + b² - 2ab·cos(C)

Solving General Triangles

Use Law of Sines or Law of Cosines to solve any triangle (not just right triangles).

Sinusoidal Equations & Models

Real-world periodic phenomena (sound waves, tides, seasons) are modeled with sine and cosine functions.

Angle Addition Identities

Example: sin(A+B) = sinA·cosB + cosA·sinB

Using Trigonometric Identities

Identities simplify complex expressions and solve equations involving trigonometric functions.

Quiz: Test Your Understanding

Which of the following is always true for any angle θ?

  1. sin(θ) + cos(θ) = 1
  2. sin²(θ) + cos²(θ) = 1
  3. tan(θ) = sin(θ) + cos(θ)

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