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Warm-Up Question

Warm-Up Question. Evaluate trigonometric functions for given angle. B. B. 1. 1. A. A. C. C. Trigonometric Functions. Trigonometric Ratios and Functions. Definitions of Trigonometric Functions. Lesson: P.570. Let be an angle in standard position, and let

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Warm-Up Question

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  1. Warm-Up Question Evaluate trigonometric functions for given angle . B B 1 1 A A C C

  2. Trigonometric Functions Trigonometric Ratiosand Functions

  3. Definitions of Trigonometric Functions • Lesson: P.570 Let be an angle in standard position, and let (x, y) be the point where the terminal side of intersects the circle . The six trigonometric functions of are defined as follows: (x, y) r • Example: P.570 Evaluate the six trigonometric functions of . (-4, 3) r Required Practice: P.571 G.P. 1, 3

  4. The Unit Circle • Lesson: P.571 The circle , which has center (0, 0) And radius 1, is called the unit circle. The values of and are simply the y-coordinate and x-coordinate, respectively, of the point where the terminal side of intersects the unit circle. (x, y) r = 1 • Example: P.571 A quadrantal angle is an angle is standard position whose terminal side lies on an axis. Use the unit circle to evaluate the six trigonometric functions of a quadrantal angle Required Practice: P.571 – G.P. 4; P.575 – 12, 13, 15

  5. Warm-Up Question For each (x, y) pair, state which quadrant the pair is located in and then evaluate sine, cosine, and tangent of the pair. (-1, 1) (1, 1) (-1, -1) (1, -1)

  6. Reference Angle Relationships • Lesson: P.572 Let be an angle in standard position. The reference angle for is the acute angle formed by the terminal side of and the x-axis.The relationship between and is shown below for nonquadrantal angles such that or Q II Q III Q IV • Example: P.571 Find the reference angle for 1) and 2) . Required Practice: P.573 G.P. 5, 6, 7, 8

  7. Sign of Trigonometric Functions • Lesson: P.572 The sign of the trigonometric functions depends on the signs of x-value and y-value in each quadrant. To evaluate trigonometric function for any angle … STEP 1: Find the reference angle . STEP 2: Evaluate the trig func for . STEP 3: Determine the sign of the trig. func. Q II: x –, y + Q I:x +, y + Q III: x –, y – Q IV: x +, y –

  8. Trigonometric Functions of Any Angle • Example: P.573 Evaluate 1) and 2) . Q II: x –, y + Q I:x +, y + Q III: x –, y – Q IV: x +, y – Required Practice: P.575 24, 25, 26, 27, 28, 29, 30, 31

  9. Homework Part 1 Workbook P.118: 1, 2, 3, 4 Part 2 Workbook P.118 – P.119: 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 18

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