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Trigonometry Chapter 6 Review

Convert angles to radians/degrees, find arc length, determine angular and linear velocity, calculate characteristics of trigonometric functions, evaluate inverse trigonometric functions, and graph trigonometric functions with given parameters.

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Trigonometry Chapter 6 Review

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  1. Chapter 6 - Trigonometry Chapter Review Presentation

  2. Chapter 6 Review Convert the given angle value into radians/degrees. Express answers in exact fraction form. Do not express as a decimal value. 1. ¼R = ________ 45 o -139/36 2. –695 o = _________ Find the length of the arc given the measure of the central angle and a radius that equals 5.0 m. 23.56 20.94 3.  = 3/2  s = _________ 4.  = 240o s = _________

  3. Chapter 6 Review Determine the angular displacement, angular velocity, and the linear velocity. Round each answer to the nearest tenth. The radius length is 5.0 m. • 3.75 revolutions in 40.0 seconds • s = __________  = __________ v = __________ 117.8 m .59 rad/sec 2.95 m/sec

  4. Chapter 6 Review Determine the characteristics of amplitude, period, horizontal phase shift , critical points and vertical phase shift. 2 6. y = 2sin(¼ + /2) – 2 amplitude = ___________, period = __________, phase shift = ________, vertical shift = _______critical points = ___________ - 2 8 - 2 -2, 0, 2, 4, 6

  5. Chapter 6 Review • y = 2cos(½ - /2) + 3 amplitude = _______, period = _______, • phase shift = ________, vertical shift = _____critical points = _____________ 2 4 , 2, 3, 4, 5  3 up

  6. Chapter 6 Review Determine the amplitude, period, horizontal phase shift, and vertical phase shift. Graph the function • y = 2cos( 3/4 + ) - 1 • amplitude = __________ period = _________ • horizontal shift = ________ vertical shift = ______ 2 8/3 -4/3 1 down

  7. Chapter 6 Review Determine the amplitude, period, horizontal phase shift, and vertical phase shift. Graph the function 10. y = -½sin( ½ - ) + 1 amplitude = ___________ period = _________ horizontal shift = _______ vertical shift = ________ -1/2 4 2 1 up 4 5 2 3 6

  8. Chapter 6 Review • Evaluate each of the following. • y = Arcsin 3/2 __ • 2. y = sin[Arccos(½)] __ • 3. y = tan( Cos –1 0 + Sin –1 ½) __ • 4. y = sin [ /2 – Sin –1 (½)] __

  9. Chapter 6 Review Find all of the values of x in degrees, 0  x  360, for which each of the following is true. 5. cot x = 0 ____________ 6. csc x = undefined _______

  10. Chapter 6 Review State the amplitude, period, and phase shift for each of the following. • y = 2tan(½- /4) • amplitude = _____, period = _______, phase shift = _______ /2 2 2 • y = ¼ csc(2 + 3/4) • amplitude = _____, period = _______, phase shift = _______ ⅜ ¼ 

  11. Chapter 6 Review Write the equation for the inverse of each function. 9. y = sin 2x ______________ 10. y = Arccos( x - /2) __________________

  12. Chapter 6 Review Graph each function for the designated domain. Show your work for all coordinates of principal values. 11. y = ½ csc(2 - /2) /4 5/4 0

  13. Chapter 6 Review Graph each function for the designated domain. Show your work for all coordinates of principal values. 12. y = Arcsin 2x -  y  0 ½ -½

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