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Warm-Up Question

Warm-Up Question. Evaluate each trigonometric function. 1) 2) 3) 4). 5) What relationship between above four values could you deduce?. Trigonometric Identities. Trigonometric Graphs, Identities, and Equations. Fundamental Trig. Identities (1/3). Lesson: P.628.

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Warm-Up Question

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  1. Warm-Up Question Evaluate each trigonometric function. 1) 2) 3) 4) 5) What relationship between above four values could you deduce?

  2. Trigonometric Identities Trigonometric Graphs, Identities, and Equations

  3. Fundamental Trig. Identities (1/3) • Lesson: P.628 A trigonometric equation thatis true for all values of the variable for which both sides of the equation are defined is called a trigonometric identities. Reciprocal Identities Tangent and Cotangent Identities • Example: P.630 Verify the identity. 1) = 1 2) = 1 Required Practice: p.632 25, 26

  4. Fundamental Trig. Identities (2/3) • Lesson: P.628 Recall that if an angle is placed on a unit circle, then r = 1 and following was true. Using the right triangle on the right, Pythagorean theorem is , which lead to following trig. Identities. Pythagorean Identities r = 1 y x • Example: P.629 Verify the identity Required Practice: p.631 G.P. 7, 9

  5. Fundamental Trig. Identities (3/3) • Lesson: P.628 Since , as you can see from the diagram, and . Similarly since , it’s clear that and . In general, we have following identities. Negative Angle Identities r = 5 (4, 3) r = 5 (4, -3) • Example: P.631 Verify the identity . Required Practice: Verify the identity a) and b) .

  6. Homework Part 1 Verify each identity. 1) 2) 3) 4) Part 2 Verify each identity. 1) 2) 3)

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