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13.7 (part 2) answers

13.7 (part 2) answers. 34) y = cos ( x – 1.5) 35) y = cos ( x + 3/(2 π )) 36) y = sin x –3 π 37) 38) y = sin ( x – 2) –4 39) y = cos ( x +3) + π 40) y = sin ( x – π /2) + 3.5 41) y = 2 cos ( x – π /3) –1 y = 2 sin ( x + π /6) –1

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13.7 (part 2) answers

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  1. 13.7 (part 2) answers 34) y = cos (x – 1.5) 35) y = cos (x + 3/(2π)) 36) y = sin x –3π 37) 38) y = sin (x – 2) –4 39) y = cos (x +3) + π 40) y = sin (x – π/2) + 3.5 41) y = 2 cos (x – π/3) –1 y = 2 sin (x + π/6) –1 42) y = 10 cos π/10(x – 10) 43) sin x = cos (x – π/2) y = 10 sin π/10(x – 5) cos x = sin (x + π/2)

  2. Section 13.8 Reciprocal Trigonometric Functions

  3. Evaluating Reciprocal Trigonometric Functions Part 1

  4. Reciprocals • We have studied sine, cosine, and tangent • These functions are ratios (fractions) and have reciprocals • These reciprocals are cosecant (csc), secant (sec), and cotangent (cot)

  5. Calculating Values Evaluate each expression: • csc (80°) 1.015 • sec (200°) –1.064 • If sin θ = 13/18, what is cscθ? 18/13 • Use the definitions of cosecant, secant and cotangent to find their values • They are the inverses of the sine, cosine and tangent values we already have

  6. More Practice Find the exact values of the following: • csc 60˚ = 1/sin 60˚ = 2√(3)/3 • sec 60˚ = 1/cos 60˚ = 2 • sec 210˚ = 1/cos 210˚ = –2√(3)/3 If sin θ = 5/13, find the other 5 trig ratios of θ. cos θ = 12/13 sec θ = 13/12 cscθ = 13/5 tan θ = 5/12 cot θ = 12/5 13 5 θ 12

  7. Homework (part 1) Please complete exercises 1 – 27 odd starting on page 752

  8. Homework (part 1) answers 1) csc (100°) = 1.02 3) cot (–55°) = –0.70 5) cot θ = 15/20 7) sec θ = –35/21 9) sec (45°) = √2 11) cot (90°) = 0 13) csc (0°) = undefined 15) cot (0°) = undefined 17) sec (90°) = undefined 19) sec (60°) = 2 21) cot (3) = –7.02 23) csc (π/2) = 1 25) sec (2.5) = –1.25 27) cot (π/6) = 1.73

  9. Graphing Reciprocal Trigonometric Functions Part 2

  10. Building a Table • Begin with the normal function • Find the reciprocal of each output value • Plot the points of the reciprocal function

  11. Plotting the Graph of y = csc (x) 1 π

  12. Using the Calculator Use the <TRACE> feature to find the following. Round your answer to the 4th decimal place. • sec (50°) 1.5557 • sec (105°) -3.8637 • csc (82°) 1.0098 • cot (20°) 2.7475 • We can use the calculator to find approximate values from graphs • We can do it using the <TRACE> or the <TABLE> feature • Begin by entering the function into Y1

  13. Homework (part 2) Please complete exercises 29– 40 starting on page 752

  14. Homework (part 2) answers 29) 30) 31) 32) 33) 1.1547 34) 5.7588 35) -2.9238 36) 2 37) 1.0642 38) 1.3054 39) 1.7321 40) 0.5774

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