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)

Reciprocal Trigonometric Functions Section 13.8 Reciprocal Trigonometric Functions

Evaluating Reciprocal Trigonometric Functions Part 1

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)

Calculating Values 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 Evaluate each expression: csc (80°) 1.015 sec (200°) –1.064 If sin θ = 13/18, what is csc θ? 18/13

More Practice csc 60˚ sec 60˚ sec 210˚ 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 csc θ = 13/5 tan θ = 5/12 cot θ = 12/5 13 5 θ 12

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

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

Graphing Reciprocal Trigonometric Functions Part 2

Building a Table Begin with the normal function Find the reciprocal of each output value Plot the points of the reciprocal function x π/6 π/2 5π/6 π 7π/6 3π/2 11π/6 2π sin (x) 0.5 1 -0.5 -1 csc (x) Undef 2 1 -2 -1

Plotting the Graph of y = csc (x) π x π/6 π/2 5π/6 π 7π/6 3π/2 11π/6 2π csc (x) Undef 2 1 -2 -1 1

Using the Calculator 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 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

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

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