SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 MATH 116 Test Review sheet SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the complement of an angle whose measure is 71. 1) ) Find the supplement of an angle whose measure is 148. ) ) Find the supplement of an angle whose measure is ) Find the measure of each angle in the problem. 4) 4) 5) 5) 6) Supplementary angles with measures x + 7 and x - degrees 6) 7) Complementary angles with measures x and 6x - 18 degrees 7) Perform the calculation. 8) ) 9) ) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 10) ) Convert the angle to degrees, minutes, and seconds. 11).66 11) Find the angle of least positive measure coterminal with the given angle. 1) ) Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 1) 98 1) 1

2 Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. 14) 50 14) 15) 95 15) Use the properties of angle measures to find the measure of each marked angle. 16) Lines m and n are parallel. 16) a = (x + 9) b = (x - 14) Find the measure of the third angle of a triangle if the measures of the other two angles are given. 17) 40 and 80 17) Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 18) 18) The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 19) B 19) The triangles are similar. Find the missing side, angle or value of the variable. 0) Q 0) a = 56 b = 6 cm

3 1) 1) a = 1 b = 1 c = 5 d = 6 e = 4 ) x ) a = 5 b = 75 c = 5 Solve the problem. Round answers to the nearest tenth if necessary. ) A tree casts a shadow 8 m long. At the same time, the shadow cast by a 7-centimeter-tall statue is 75 cm long. Find the height of the tree. ) Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 4) (-, 5) 4) Suppose that is in standard position and the given point is on the terminal side of. Give the exact value of the indicated trig function for. 5) (-5, 1); Find sin. 5) An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the indicated trigonometric function value of. Do not use a calculator. 6) -9x + y = 0, x 0; Find sin. 6)

4 Evaluate the expression. 7) sec(-180 ) 7) If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. 8) III, x y 8) Evaluate the expression. 9) cos 0 - sin 90 9) Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. 0) cos, given that sec = -7 0) Identify the quadrant for the angle satisfying the following conditions. 1) cos < 0 and csc < 0 1) Decide whether the statement is possible or impossible for an angle. ) tan = -1.6 ) Use the fundamental identities to find the value of the trigonometric function. ) Find sin, given that cos = and is in quadrant IV. ) 4) Find csc, given that cot = - 15 and is in quadrant II. 4) Evaluate the function requested. Write your answer as a fraction in lowest terms. 5) 5) Find tan A. Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. 6) Find tan B when a = 48 and c = 50. 6) Without using a calculator, give the exact trigonometric function value with rational denominator. 7) sec 45 7) 4

5 Solve the problem. 8) Find the exact value of x in the figure. 8) 40 Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. 9) sin( + 14 ) 9) Find a solution for the equation. Assume that all angles are acute angles. 40) sec = csc( + 46 ) 40) Decide whether the statement is true or false. 41) sin 86 > sin 4 41) Solve the problem for the given information. 4) Find the equation of a line passing through the origin and making a 45 angle with the positive x-axis. 4) Find the reference angle for the given angle. 4) 19 4) Find the exact value of the expression. 44) cot 60 44) 45) sec ) 46) sin 85 46) Evaluate. 47) tan 10 + sin cos 0 47) Find the sign of the following. 48) cos ( ), given that is in the interval (90, 180 ). 48) Find all values of, if is in the interval [0, 60 ) and has the given function value. 49) sec = - 49) 5

6 50) sin = 50) 6

7 Answer Key Testname: MATH 116 TEST 1 1) 19 ) ) ) 100 and 80 5) 40 and 50 6) 77 and 10 7) 6 and 54 8) ) ) ) 9 6 1) 44 1) 98 + n 60 14) 410 and ) 655 and ) 55, 55 17) 60 18) Right, scalene 19) T 0) 56 1) x = 10 ) x = 9 ) 18.7 m 4) 5) 1 1 7

8 Answer Key Testname: MATH 116 TEST 1 6) ) -1 8) Positive 9) - 0) ) Quadrant III ) Possible 5 ) - 4) 4 5) tan A = 5 1 6) 7 4 7) 8) 0 6 9) cos(76 - ) 40) 41) True 4) y = x 4) 51 44) 45) - 46) - 47) 11 48) positive 49) 15 and 5 50) 60 and 10 8