# Find the coterminal angle from [0, 360◦ ) or [0, 2π), complement and supplement (from coterminal angle)

## Find the coterminal angle from [0, 360◦ ) or [0, 2π), complement and supplement (from coterminal angle)

Find the coterminal angle from [0, 360◦ ) or [0, 2π), complement and supplement (from coterminal angle), and the quadrant of the following angles and draw the coterminal angle in standard position. Keep answers in the form (radians or degrees) of their original question. a 156◦ i Coterminal Angle: ii Complement: iii Supplement: iv Quadrant: v Draw Angle b − 7π 3 i Coterminal Angle: ii Complement: iii Supplement: iv Quadrant: v Draw Angle c 1070◦ i Coterminal Angle: ii Complement: iii Supplement: iv Quadrant: v Draw Angle d − 5π 3 i Coterminal Angle: ii Complement: iii Supplement: iv Quadrant: v Draw Angle 1 2. In 1-2 sentences, describe a radian. 3. Two pulleys are connected by a belt so that when one pulley rotates, the linear speeds of the belt and both pulleys are the same. The radius of the smaller pulley is 4 inches, and the radius of the larger pulley is 5 inches. A point on the belt travels at a rate of 400 inches per minute. a Find the angular speed of the larger pulley b Find the angular speed of the smaller pulley 4. A bicycle with wheels 28 inches in diameter is traveling at the rate of 5 feet per second. What is the angular speed of the wheels? How many rotations do the tires make per second? Round answers to 2 decimal places. 2 5. An old vinyl record is played on a turntable rotating clockwise at a rate of 45 rotations per minute. Find the angular speed in radians per second. If the record has a diameter of 6 inches, find the linear speed of a point on the tip of the record. 6. The wheel of a truck has the diameter of 22in and the wheel of a coup has a diameter of 16in. If the coup has the angular speed of 3 rad/sec and the truck has the angular speed of 2 rad/sec, which vehicle is moving faster? How can you tell? Include the linear speeds in your answer and use them as evidence to support your answer. 3 7.2 Name: You must show all your work to get full credit. Round answers to 2 decimal places unless otherwise specified. For the triangles in questions 1-5, remember that ABC refers to the angles and a, b, c refers to the side lengths (opposing the associated angle). 1. For the triangle ABC (C=90◦ ) where A=32◦ and c=200in, find a 2. For the triangle ABC (C=90◦ ) where a=40m and c=76m, find B 3. For the triangle ABC (C=90◦ ) where b=35in and a=55in, find A 4. Solve the triangle ABC (C=90◦ ) where A=57◦ and c=21ft 5. Solve the triangle ABC (C=90◦ ) where A=26◦ and a=24m 4 6. Two friends are on opposite sides of a river. To find the width of the river, each of them hammered a stake on his bank of the river in such a way that the distance between the two stakes approximates the width of the river. One of the friends walks 140 feet away from his stake along the river and finds that the line of sight from his new position to his friend’s stake across the river and the line of sight to his own stake form a 40◦ angle. How wide is the river? Round answer to 2 decimal places. 7. How tall is a building that casts a 72-ft shadow when the angle of elevation from the end of the shadow to the top of the building is 31◦ ? Round answer to the nearest foot. 8. An airplane is flying at an altitude of 3967 ft. The slanted distance directly to the airport is 16,999 ft. How far is the airplane horizontally from the airport? Round your answer to the nearest foot. 5 9. To find the height of a tree, a person walks to a point 30 feet from the base of the tree. She measures an angle of 57o between a line of sight to the top of the tree and the ground. Find the height of the tree to the nearest foot. 10. Suppose a building is erected such that the base of the building is 100m from the base of a tower. The angle of elevation from the top of the building to the top of the tower is 80.38◦ and the angle of depression from the top of the building to the foot of the tower is 65.05◦ . How tall is the building? The tower? Round answers to the nearest meter. 6 7.3 Name: You must show all your work to get full credit 1. Show that − √ 3 2 , 1 2 ! is on the unit circle. 2. Let x be the measure of an angle with a terminal side that goes through the point − √ 3 2 , 1 2 ! . Find the following: sin(x) csc(x) cos(x) sec(x) tan(x) cot(x) 3. Find the following: sin − π 2 csc − π 2 cos − π 2 sec − π 2 tan − π 2 cot − π 2 7 4. Show that − √ 2 2 , − √ 2 2 ! is on the unit circle. 5. Let x be the measure of an angle with a terminal side that goes through the point − √ 2 2 , − √ 2 2 ! . Find the following: sin(x) csc(x) cos(x) sec(x) tan(x) cot(x) 6. Find the following: sin 13π 6 csc 13π 6 cos 13π 6 sec 13π 6 tan 13π 6 cot 13π 6 8 7.4 Name: You must show all your work to get full credit 1. Is (2, −1) on the unit circle? Prove your answer mathematically. 2. Let x be the measure of an angle with a terminal side that goes through the point (−2, 1), find the following sin(x) csc(x) cos(x) sec(x) tan(x) cot(x) 3. If secθ = − 5 4 and sin > 0, find the following sin(θ) csc(θ) cos(θ) sec(θ) tan(θ) cot(θ) 9 4. Is 1 2 , − 1 2 on the unit circle? Prove your answer mathematically. 5. Let x be the measure of an angle with a terminal side that goes through the point 1 2 , − 1 2 , find the following sin(x) csc(x) cos(x) sec(x) tan(x) cot(x) 6. If sinθ = 3 5 and tan < 0, find the following sin(θ) csc(θ) cos(θ) sec(θ) tan(θ) cot(θ) 10 7. For the following angles, find the reference angles and draw a sketch of the original angles. Don’t forget to find coterminal angles where applicable. a 2π 3 i Sketch the angle ii Reference angle θ 0 b −170◦ i Sketch the angle ii Reference angle θ 0 c 700◦ i Sketch the angle

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