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Trigonometric Identities

Section 14-1. Trigonometric Identities. There are six trigonometric ratios that we will deal with in Chapter 14. sine ratio (sin θ ) cosine ratio (cos θ ) tangent ratio (tan θ ) cosecant ratio (csc θ ) secant ratio (sec θ ) cotangent ratio (cot θ ). Example 1.

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Trigonometric Identities

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  1. Section 14-1 Trigonometric Identities

  2. There are six trigonometric ratios that we will deal with in Chapter 14. • sine ratio (sin θ) • cosine ratio (cos θ) • tangent ratio (tan θ) • cosecant ratio (csc θ) • secant ratio (sec θ) • cotangent ratio (cot θ)

  3. Example 1 • Verify each identity.

  4. To verify an identity is to get the left side of the equation to look the right side of the equation using the trigonometric identities formulas.

  5. 1st step: Substitute for cot θ using the cotangent identity.

  6. 2nd step: Multiply cos θ and the fraction to make one fraction. 3rd step: Realize that cos2θ + sin2θ = 1 can be rewritten as cos2θ = 1 – sin2θ and substitute in the numerator.

  7. 4th step: Rewrite the one fraction as two fractions. Final step: Simplify.

  8. Example 2 • Simplify each trig expression. • 1. tan θ cot θ • 2. sec2θ – 1 • 3. sec θ cot θ • 4. sin θ cot θ • 5. sec θ cos θ sin θ

  9. 1. tan θ cot θ

  10. 2. sec2θ – 1 • We can rewrite 1 + tan2θ = sec2θ as • tan2θ = sec2θ – 1 • sec2θ – 1 = tan2θ

  11. 3. sec θ cot θ

  12. 4. sin θ cot θ

  13. 5. sec θ cos θ sin θ

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