Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179

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1 Trigonometry Chapters 1 & 2 Test 1 Name Provide an appropriate response. 1) Find the supplement of an angle whose measure is 7. Find the measure of each angle in the problem. 2) Perform the calculation. ) ) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 5) Convert the angle to degrees, minutes, and seconds. 6) Find the angle of least positive measure coterminal with the given angle. 7) 877 8) -61 Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179 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. 10) 10 Solve the problem. 11) A wheel makes 72 revolutions per minute. How many revolutions does it make per second? 1

2 12) Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that cuts off the same arc. See the figure.) Use the properties of angle measures to find the measure of each marked angle. 1) Lines m and n are parallel. a = (x + 26) b = (4x - 17) Find the measure of the third angle of a triangle if the measures of the other two angles are given. 14) 22 and 20 Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 15) 16) The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 17) C 2

3 18) AC (AB is parallel to DE.) 19) U (RS is parallel to UV.) The triangles are similar. Find the missing side, angle or value of the variable. 20) x a = 25 b = 75 c = 52 Solve the problem. Round answers to the nearest tenth if necessary. 21) A tree casts a shadow 16 m long. At the same time, the shadow cast by a 62-centimeter-tall statue is 9 cm long. Find the height of the tree. 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. 22) III, x y Use the fundamental identities to find the value of the trigonometric function. 2) Find sin θ, given that cos θ = 2 and θ is in quadrant IV.

4 24) Find tan θ, given that sin θ = and θ is in quadrant II. 4 25) Find sec θ, given that tan θ = 4 and θ is in quadrant I. Evaluate the function requested. Write your answer as a fraction in lowest terms. 26) Find sin 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. 27) Find csc A when b = 40 and c = 85 28) Find sin A when a = 7 and b = 6. Without using a calculator, give the exact trigonometric function value with rational denominator. 29) tan 60 Solve the problem. 0) Find the exact value of x in the figure. 14 x Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. 1) tan 24 2) cos 1.9 Find a solution for the equation. Assume that all angles are acute angles. ) sec(θ + 15 ) = csc(2θ + 9 ) 4

5 Solve the problem for the given information. 4) Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant I and the positive x-axis is 2. Find the reference angle for the given angle. 5) 108 6) 247. Find the exact value of the expression. 7) cos 210 8) cos 1200 Find all values of θ, if θ is in the interval [0, 60 ) and has the given function value. 9) sin θ = 2 Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. 40) sin Find a value of θ in [0, 90 ] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. 41) tan θ = Solve the problem. 42) Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the radar speed reading is the product of the actual reading and the cosine of the angle. Find the radar reading to the nearest hundredth for the auto shown in the figure. 9 angle Actual speed: 87 mph 4) If an automobile is traveling at velocity V (in feet per second), the safe radius R for a curve with superelevation V2 α is given by the formula R =, where f and g are constants. A road is being constructed for g(f + tan α) automobiles traveling at 5 miles per hour. If α = 4, g = 0.5, and f = 0.16, calculate R. Round to the nearest foot. (Hint: 1 mile = 5280 feet) 5

6 44) The index of refraction for air, Ia, is The index of refraction for water, Iw, is 1.. If I w Ia = sin A sin W, and A = 1.5, find W to the nearest tenth. Solve the right triangle. If two sides are given, give angles in degrees and minutes. 45) a = 20. cm, b = 20.8 cm Round the missing side length to one decimal place. An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. 46) (7, 0) Solve the problem. 47) A 5.2-ft fence is ft away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find θ, the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree when necessary. 5.2 ft ft 6

7 Answer Key Testname: TRIGPRACTICETEST1 1) 14 2) 0 and 60 ) ) ) ) ) 157 8) 299 9) n 60 10) 70 and ) 6.2 revolutions per second 12) 60 1) 155, ) 18 15) Right, scalene 16) Obtuse, isosceles 17) R 18) EC 19) S 20) x = 9 21) 10.7 m 22) Positive 2) ) ) ) sin A = ) ) ) 0) ) cot 66 2) sin 58.1 ) 22 4) y = x 5) 72 6) 67. 7) - 2 7

8 Answer Key Testname: TRIGPRACTICETEST1 8) ) 60 and ) ) ) 85.9 mph 4) R = 862 ft 44) ) A = 44 18'; B = 45 42'; c = 29.1 cm 46) 90 ; N 90 E or S 90 E 47) θ =

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