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Proving Trigonometric Identities: Counter Example for sin(x)cos(x) = tan(x)

This lesson addresses the concept of counterexamples in proving trigonometric identities. We focus on demonstrating that the equation sin(x)cos(x) = tan(x) is not an identity by using a specific counterexample. By letting x = 45°, we calculate sin(45°)cos(45°) = 0.5 and tan(45°) = 1, leading to the conclusion that 0.5 ≠ 1. This proves that the given equation does not hold for all values of x, specifically at 45°. Continue practicing with examples to deepen your understanding of trigonometric identities.

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Proving Trigonometric Identities: Counter Example for sin(x)cos(x) = tan(x)

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  1. Agenda • Proving by Counter Example

  2. Trigonometric Identities 3/22 A counter example is an example that proves something does NOT work • Counter Example

  3. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example • Counter Example

  4. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = 0.5 tan 45o = 1 • Counter Example

  5. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = • Counter Example

  6. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = 0.5 • Counter Example

  7. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = 0.5 tan 45o = • Counter Example

  8. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = 0.5 tan 45o = 1 • Counter Example

  9. Trigonometric Identities 3/22 Prove that sin xcosx = tan x is not an identity by producting a counter example let x = 45o sin 45ocos 45o = 0.5 tan 45o = 1 0.5 =/= 1 Not an identity • Counter Example

  10. Classwork • Continue on your classwork page • Complete # 18-23 on page 427 • You have 15 minutes to finish

  11. Trigonometric Identities 3/22 Use the appropriate trigonometric identity to find the value you are asked for. Example: • Determining an exact value

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