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Algebra 2 Chapter 13 Test Review 1 Name: ______________ Date_______Per The diagram below shows right triangle UPC. Evaluate the following: sin U = csc U = cos U = sec U = tan U = cot U = 2 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 45 degrees and radius a) What is the length of arc AC, in feet? feet. (Give exact answer.) b) What is the area of the sector? 3. Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures radians, what is the length, in yards, of the border? 4 As shown in the accompanying diagram, a dial in the shape of a semicircle has a radius of 4 centimeters. Find the measure of θ, in radians, when the pointer rotates to form an arc whose length is 1.38 centimeters. 6) Express 330º in radian measure. 7) Express 330º in radian measure. 8) Express 9) Express radians in degree measure. radians in degree measure. 10 List a positive angle between 0º and 360º that is coterminal to 985º. 11 List a negative angle between 0 and -2π radians that is coterminal to 7𝜋 2 . 12 Circle all angles that are coterminal to 1125⁰. a. g. 60⁰ 9𝜋 4 b. -45⁰ h. 5𝜋 4 c. 45⁰ i. −𝜋 4 d. 445⁰ 𝜋 j. 4 e. 820⁰ k. −7𝜋 4 For problems 13-16, find the length of each missing side in simplest radical form. f. 765⁰ l. −15𝜋 4 For problems 17-22, evaluate using the Unit Circle. Label the diagram, label the reference angle, and label the sides before evaluating. Give exact answers. No decimals. Rationalize denominators. 5𝜋 17) sin 180⁰ 18) cos 6 19) cot(-330⁰) 20) csc 60⁰ 21) sec 3𝜋 22) tan 135⁰ 2 For #23-28, sketch the graph of each circle. Identify the radius of the circle. 23. (𝑥 + 1)2 + (𝑦 − 1)2 = 16 24. 2𝑥 2 + 2𝑦 2 = 10 radius: ______ radius: ______ center : (___, ____) center (____, _____) Write the equation of each circle. 25. 27. Passes through (-6, 8) with center at (0, 0) 26. 28. Passes through (-8, -5) with center at (0, 0)