MATH 113 PRACTICE TEST 1 PART 1 FALL 2007

Transcription

1 MATH PRACTICE TEST PART FALL 007 Do not use a calculator or computer on this part of the test. Turn off and put awa cell phones. In addition to these problems, be able to do a graph like the one in eample on page 50, and be able to graph the inverse trigonometric functions on page 5. The given angle is in standard position. Determine the quadrant in which the angle lies. ) - Solve the problem. ) Use the figure below to determine the radian measure of angle θ. ) 9 ) -5 Name the quadrant in which the angle lies. ) 7 5) - ) Classif the angle as acute, right, obtuse, or straight. 7) ) Find the radian measure of the central angle θ which intercepts a 5 cm arc in a circle of radius 5 cm. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. ) r = feet, s = 7 feet 5) r = meter, s = 00 centimeters ) Convert the angle in degrees to radians. Epress answer as a multiple of. ) 5 7) -90 9) ) 5 9) - 0 Convert the angle in radians to degrees. 0) 0) ) - 5 Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. ) r = inches, s = 0 inches ) - 5 9

2 Find a positive angle less than 0 that is coterminal with the given angle. ) - Find the eact value of the indicated trigonometric function for the given right triangle. ) ) 5) -5 ) 5 sin θ 7) 0 ) ) Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give an eact answer with a rational denominator. 9) csc θ ) Find sin θ. 5 0) cot θ Find csc θ. ) 9 A point on the terminal side of angle θ is given. Find the eact value of the indicated trigonometric function of θ. 5) (5, 0) Find sin θ. ) (-0, ) Find sin θ. 7) (, ) Find csc θ. ) (-5, ) Find tan θ. 9) (, -) Find sin θ. Find tan θ. 0) (-, -) Find sec θ.

3 Evaluate the trigonometric function at the quadrantal angle, or state that the epression is undefined. ) cos 5) cot 0 59) sec 0 ) sec 0) sec 50 ) csc 0 ) tan ) csc 0 ) sin ) sin Without using a calculator, give the eact trigonometric function value with rational denominator. 5) sin 0 ) cos 7) cos 0 Use reference angles to find the eact value of the epression. Do not use a calculator. ) tan 5 5) cot -9 Give the eact value. ) sin ) cos 5 9) tan 0 7) tan 5 50) tan 5) cot 5 Use a reference angle to find the eact value of the epression. ) cos (-0 ) 5) sec 5) csc 5 5) sec 9) sin (-0 ) 70) sin -0 7) cos 90 7) cos 0 Give the eact value. 55) cos 0 7) sin -00 5) cos 50 7) sin 7 57) tan 00 75) cos

4 Find the eact trigonometric function value. 7) csc 0 77) csc (-70 ) 7) sec 55 79) cot (-55 ) 0) cos (-0 ) Find the eact function value. ) cos 95) -0 9) 0 97) -5 9) The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 99), 55 Find sin t. ) cot 00) 9, 77 9 Find tan t. Find the eact function value if it eists. ) csc 0 0) - 9, 5 Find cos t. ) csc 90 5) csc 70 0) 7, Find sec t. ) cos (-90 ) 0) , - 9 Find sin t. 7) csc (-0 ) Find the eact value of the indicated trigonometric function of θ. ) tan θ = -, 90 < θ < 0 Find cos θ. 5 Solve the problem. 0) What is the domain of the cosine function? 05) What is the range of the cosine function? 9) cos θ = 5 7, < θ < Find cot θ. 90) cot θ = - 7, cos θ < 0 Find csc θ. Sin t and cos t are given. Use identities to find the indicated value. Where necessar, rationalize denominators. 0) sin t = -, cos t = - 5. Find cot t. 9) csc θ = - 5, θ in quadrant III Find cot θ. 07) sin t =, cos t = 5. Find sec t. Find the reference angle for the given angle. 9) 9 0) sin t = - 7, cos t = 5. Find tan t. 7 9) - 9) -9

5 0 t < and sin t is given. Use the Pthagorean identit sin t + cos t = to find cos t. 09) sin t = ) = - sin - ) = 5 cos ( + ) Use an identit to find the value of the epression. Do not use a calculator. 0) sin.7 csc.7 5) = 5 - sin + ) = - sin 5 - ) sin + cos Find a cofunction with the same value as the given epression. ) sin 7 ) cos 7 Graph. Show as much of the graph as possible on the given diagram. 7) = - cos ) tan 5 5) csc 0 ) sin ) = sin 7) tan Find the amplitude or period. ) Find the amplitude of = -5 sin +. 9) Find the period of = 5 sin +. 0) Find the period of = cos ) Find the period of = sin -. Find the phase shift of the function. ) = sin +

6 9) = cos - Graph the function. Show as much of the graph as possible on the given diagram. ) = sin ) = sin - Graph the function. Show asmptotes. ) = tan Graph. ) = sin - ) = cot

7 5) = csc + ) cos- - ) cos- (-) ) tan- ) tan- () - 7) tan- 0 ) f(t) = sec t Find the eact value of the epression, if possible. Do not use a calculator. ) sin- sin 7 9) tan- tan t 50) cos- cos - 5) cos- cos - Find the eact value of the epression without using a calculator or table. 7) sin- Use a sketch to find the eact value of the epression. 5) cot sin- 0 0 ) cos- 9) sin- (-0.5) Find the eact value of the epression. 0) sin- 5) sin tan- - Use a right triangle to write the epression as an algebraic epression. Assume that is positive and in the domain of the given inverse trigonometric function. 5) sin(tan- ) 55) cos(sin- ) ) sin- Evaluate. ) cos- 5) cos- cos 7 57) sin- sin

8 Answer Ke Testname: MATH PRACTICE TEST PART ) Quadrant I ) Quadrant II ) Quadrant IV ) II 5) I ) III 7) right ) acute 9) obtuse 0) straight ) 5 radians ) radians ) radians ) radians 5) radians ) radians 7) - radians ) 0 radians 9) - radians 0) 0 ) - ) -700 ) ) 5) 05 ) 7) ) 0 9) sin θ = 9 9 0) csc θ = 5 9 ) tan θ = ) 7 ) 5 7 )

9 Answer Ke Testname: MATH PRACTICE TEST PART 5) 5 ) 7) 5 ) - 5 9) ) - 5 ) - ) undefined ) undefined ) 5) ) 7) ) 9) 50) 5) 5) 5) 5) 55) - 5) - 57) - 5) - 59) - 0) - ) - ) - )

10 Answer Ke Testname: MATH PRACTICE TEST PART ) 5) ) - 7) - ) - 9) - 70) 7) 7) 7) 7) - 75) - 7) 77) 7) - 79) 0) ) ) Not defined ) Undefined ) 5) - ) 0 7) ) ) ) 9) 5

11 Answer Ke Testname: MATH PRACTICE TEST PART 9) 9) 9) 9 95) 0 9) 0 97) 5 9) 99) 55 00) 0) ) 7 7 0) - 9 0) all real numbers 05) all real numbers from - to, inclusive 0) 5 07) 5 0) ) 5 0) ) ) cos ) sin 7 ) cot 5) sec 0 ) cos 5 7) cot 5 ) 5 9) 0) ) ) - )

12 Answer Ke Testname: MATH PRACTICE TEST PART ) - 5) - ) 0 7) ) )

13 Answer Ke Testname: MATH PRACTICE TEST PART 0) ) ) ) - - -

14 Answer Ke Testname: MATH PRACTICE TEST PART ) ) - ) - t - - 7) ) 9) - 0) )

15 Answer Ke Testname: MATH PRACTICE TEST PART ) ) ) 5) ) 7) 0 ) 7 9) ) 5) 5) 5) - 5 5) ) - 5) 5 57)