Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places.

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1 SECTION.1 Simplify. 1. 7π π. 5π 6 + π Find the measure of the angle in degrees between the hour hand and the minute hand of a clock at the time shown. Measure the angle in the clockwise direction.. 1:0. 5:0 Find the area of the circle with the given radius. 5. r = in. 6. r = 1.5 ft Determine the quadrant in which each angle lies. Then convert the angle measure from radians to degrees. Round to two decimal places. 1. π π. Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round to two decimal places. 7. r = 11 in.; θ = 100º 5. r =.6 ft; θ = 90º 6. r = 0 cm; θ = π ANSWERS WU 1. π. 7π º. 70º 5. 9π in. 6..5π ft QUIZ 1. Quadrant I; 7º. Quadrant I; º. Quadrant II; 1.69º in ft cm

2 SECTION. Rewrite each angle in degree measure. (Do not use a calculator.) 1. π. 10π. 1π 6 Classify each function as odd, even, or neither. 5. f(x) = 6x + x 6. g(x) = x 7. f(x) = x 8x. π 1 Evaluate (if possible) the six trigonometric functions of the real number. 1. t = π. t = 11π 6. t = π Use the value of the trigonometric function to evaluate the given functions.. sin t = 0.8 (a) sin ( t) (b) csc t 5. cos ( t) = 5 (a) cos (! t) (b) sec t 5

3 ANSWERS WU 1. 15º. 600º º 5. odd 6. even 7. neither QUIZ 1. sin π = ; cos π = ; tan π = 1; csc π = ; sec π π = ; cot = 1. sin 11π 6 = 1 11π ; cos 6 = 11π ; tan 6 = ; csc 11π 6 11π = ; sec 6 = 11π ; cot 6 =. sin π = ; cos π = 1 ; tan π = ; csc π = ; sec π π = ; cot =. (a) 0.8 (b) (a) 5 (b) 5 6

4 SECTION. The lengths of the legs of a right triangle are given. Find the length of the hypotenuse. 1. cm, 5 cm. in., 6 in. Evaluate (if possible) the six trigonometric functions of the real number.. t = 5π. t = π 5. t = π 6 1. Find the exact values of the six trigonometric functions of the angle θ for the triangle. Use trigonometric identities to transform the left side of the equation into the right side (0 < θ <!/).. tan α csc α = sec α. sinθ + cotθ cosθ = cscθ 7

5 ANSWERS WU 1. cm. 10 in.. sin 5π = ; cos 5π = ; tan 5π = 1; csc 5π = ; sec 5π 5π = ; cot = 1. sin π = 1; cos π = 0; csc π = 1; cot π = 0 5. sin π 6 = 1 ; cos π 6 = ; tan π 6 = ; csc π 6 = ; sec π 6 = ; cot π 6 = QUIZ 1. sinθ = 10 ; cosθ = ; tanθ = ; cscθ = ; secθ = ; cotθ = 0. tan α csc α = sin α 1 cos α sin α = 1 cos α = sec α. sinθ + cotθ cosθ = sinθ + cosθ sinθ (cosθ) = sinθ + cos θ sinθ = sin θ sinθ + cos θ sinθ = sin θ + cos θ = 1 sinθ sinθ = cscθ 8

6 SECTION. Determine the quadrant in which each angle lies º. 0º. 9º Find the values of θ in degrees (0º < θ < 90º) and radians (0 < θ <!/) without the aid of a calculator.. cosθ = 5. tanθ = 6. cscθ = Find the values of the six trigonometric functions of θ with the given constraint. 1. tan θ = ; θ lies in Quadrant III.. sin θ = 1 6 ; cos θ > 0. sec θ is undefined;! < θ <! Evaluate the sine, cosine, and tangent of the angle without using a calculator.. 0º 5. 9π 9

7 ANSWERS WU 1. Quadrant I. Quadrant III. Quadrant IV. 0º, π º, π º, π QUIZ 1. sinθ = ; cosθ = ; tanθ = ; cscθ = ; secθ = ; cotθ = 1. sinθ = ; cosθ = ; tanθ = ;. cscθ = 6; secθ = ; cotθ = 5 sinθ = 1; cosθ = 0; cscθ = 1; cotθ = 0. sin 0 = ; cos 0 = 1 ; tan 0 = 5. sin 9π = ; cos 9π = ; tan 9π = 1 0

8 SECTION.5 Evaluate the trigonometric function of the quadrant angle. 1. cos π. sin π Find two solutions of the equation. Give your answers in radians (0 < θ <!).. cos(θ) = 1. sin(θ) = 5. cos(θ) = 0 Find the period and amplitude. 1. y = cosπx. y = sin x Sketch the graph of the function. (Include two full periods.). y = cos(x π ). y = πx sin + 5. y = 1 cos(x) 1

9 ANSWERS WU π, π. π, π 5. π, π QUIZ 1. ;.. ; π. 5.

10 SECTION.6 Sketch the graph of the function. (Include two full periods.) 1. y = sin(πx). y = + cos(x π ). y = 1 sin x π Find the period and the amplitude of the trigonometric function.. y = 5cos πx 5. y = sin(x + π ) 6. y = cos(x) Sketch the graph of the function. (Include two full periods.) 1. y = tanπx 1. y = 1 sec x + π. y = + cot(πx) Use a graph to solve the equation on the interval [!,!].. cot x = 1 5. sec x = 6. csc x =

11 ANSWERS WU 1... π. 6; 5 5. ; 1 6. π; QUIZ 1..

12 .. 5π, π, π, 7π 5. 11π 6, π 6, π 6, 11π π 6, π 6, 7π 6, 11π 6 5

13 SECTION.7 Use the properties of inverse functions to evaluate the expression. 1. f 1 (f( )). f(f 1 (1)) Expressions representing the legs of a right triangle are given. Write an expression to represent the hypotenuse.. 5x;. (x ); x Use a calculator to evaluate the expression. Round your result to two decimal places. 5. sin csc ( ) 7. cot (11º) Evaluate the expression without using a calculator. 1. arccos 1. tan 1 Find the exact value of the expression. (Hint: Sketch a right triangle.). tan arccos 5. csc tan 1 () Write an algebraic expression that is equivalent to the expression. 5. sin (arccos x) 6. cot arcsin x ANSWERS WU x + 9. x x QUIZ π x 6. x 6

14 SECTION.8 Use a calculator to evaluate the expression. Round your result to two decimal places. 1. arccos 0.7. arctan. sin tan 1 ( 1.5) 5. A child holds a balloon in her hand at a height of feet. The balloon is attached to a 5-inch string, and the wind blows the balloon so the string forms an angle θ from vertical. Write θ as a function of the height h of the balloon, in inches. 1. The sun is 1º above the horizon. Find the height of a road sign that casts a shadow 18 feet long. Round your answer to two decimal places.. An airplane is 10 miles south and 5 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Round your answer to two decimal places.. A piece of paper measures 8 inches by 10 inches. A corner is folded over so that it touches the long side at its midpoint. What is the angle formed by the corner and the long side? Round your answer to the nearest degree. ANSWERS WU h θ = cos 1 5 QUIZ ft. N.0 E. 6 7