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TRIGONOMETRY

Understand trigonometric ratios for angles like 30ᵒ, 45ᵒ, and 60ᵒ with easy-to-follow steps and helpful mnemonics. Learn about reference angles, solving equations, and identities in trigonometry.

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TRIGONOMETRY

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  1. TRIGONOMETRY

  2. Trigonometric Ratio c Figure 1 b  a

  3. Trigonometric Ratio (cont) c b  a

  4. Trigonometric Ratio (cont) A 5 3  C B 4

  5. Trigonometric Ratio (cont) A 9.327 cm 73.2ᵒ C B

  6. Trigonometric Ratio (cont) A 21.52cm 53.2ᵒ 31.5ᵒ D B C

  7. Trigonometric ratio for angles: 30ᵒ, 45ᵒ and 60ᵒ C Consider an equilateral triangle ABC with sides of 2 units length. Trigo ratio of 30ᵒ : Trigo ratio of 60ᵒ: 30ᵒ 30ᵒ 2 2 60ᵒ 60ᵒ B A 1 D 1

  8. Trigonometric ratio for angles: 30ᵒ, 45ᵒ and 60ᵒ (cont) C Consider an isoceles triangle ABC. The two sides AB and BC are of 1 unit length. Trigo ratio of 45ᵒ : 45ᵒ 1 45ᵒ A B 1

  9. Trigonometric ratio for angles: 30ᵒ, 45ᵒ and 60ᵒ (cont)

  10. Trigonometric ratio for angles: 30ᵒ, 45ᵒ and 60ᵒ (cont)

  11. The Sign of trigonometric Ratio of any angle in four quadrants of a Cartesian Plane y 1st Quadrant sine (+ve) cosine (+ve) tangent (+ve) 2nd Quadrant sine (+ve) cosine (-ve) tangent (-ve) x 0 3rd Quadrant sine (-ve) cosine (-ve) tangent (+ve) 4th Quadrant sine (-ve) cosine (+ve) tangent (-ve) Mnemonic: A S T C (Are School Tests Crazy?)

  12. Reference Angle

  13. Reference Angle (cont)

  14. Reference Angle (cont)

  15. Solving Trigonometric Equations Step 1: What is the domain given? Step 2: Find the reference angle Step 3: Find other angles in the correct quadrant (+ve/-ve) Step 4: Write down all your answers clearly

  16. Solving Trigonometric Equations (cont)

  17. Trigonometric Identities

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