2.Draw each angle in standard position. Name the quadrant in which the angle lies. 2. Which point(s) lies on the unit circle? Explain how you know.

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1 Chapter Review Section.1 Extra Practice 1.Draw each angle in standard position. In what quadrant does each angle lie? a) 1 b) 70 c) 110 d) 00.Draw each angle in standard position. Name the quadrant in which the angle lies. a) b) c) d).change the degree measures to radians. Give answers as both exact and approximate measures to the nearest hundredth of a unit. a) 10 b) 0 c) d) 10.Change the radian measures to degrees. Round to two decimal places if necessary. a) b) c) 11 1 d) 7.Change the radian measures to degrees rounding to the nearest whole degree. a). b) c) d)..determine the two subsequent positive angles that are coterminal with the given angle. Round approximate measures to the nearest hundredth of a unit. a) 0 b) c) Explain how you would find the subsequent negative angle that is coterminal with each given angle. a) 0 b) 9 c) Write an expression for all the angles that are coterminal with each given angle. a) 7 b) c) 1 9.A circle with a radius of 1. cm is drawn on a large piece of cardboard. A central angle of 7 is drawn. What is the length of the arc subtended by this angle rounded to the nearest tenth of a cm? 10.The radius of a circle is 7 cm and the length of an arc on the circle is 10 cm. In radians what is the central angle that subtends this arc length? Give your answer to the nearest hundredth of a unit. Section. Extra Practice 1. Write the equation of a circle with the given radius and its centre at (0 0). a) units b) units c) 9.1 units d) 11 units. Which point(s) lies on the unit circle? Explain how you know. ( 1 1 ) ( ). Each of the following points lies on the unit circle. Find the missing coordinate satisfying the given conditions. a) ( ) ( ) in I b) c) y x in y in quadrant IV d) 1 x in quadrant I 7.The point P(x y) is located where the terminal arm of angle θ and the unit circle intersect. Determine the coordinates of point P for the given angle. a) θ = b) θ = 70 c) θ = 0 d)θ = 10. The point P(x y) is the point at the intersection of angle θ. If P(θ) is the point at the intersection of the terminal arm of angle θ and the unit circle determine the exact coordinates of each. P b) P a) ( ) ( ) c) P() d) 11 P. Identify a measure for θ in the interval 0 θ < 0 such that P(θ) is the given point. a) c) b) (1 0) d) 1 7. Identify a measure for θ in the interval 0 θ < such that P(θ) is the given point. 1 a) (1 0) b) c) 1 d) (1 0)

2 8. On a diagram of the unit circle show all the integral multiples of in the interval 0 θ <. On your diagram label the coordinates for each point P(θ) Consider a point where P( θ ) =. a) Determine the coordinates of P θ+. b) Determine the coordinates of 10. If P( θ ) = determine the following. a) the coordinates of P θ+ b) the coordinates of P θ Section. Extra Practice 1. What is the exact value of each trigonometric ratio? a) sin 0 b) cos 0 c) tan 1 d) sin 70 e) csc 0 f ) sec 180. Determine the exact value of each of the following. a) cot b) d) cos e) 7 sin c) sec csc tan f ). Determine the approximate value for each trigonometric ratio to the nearest hundredth of a unit. a) sin 0 b) cos 1 c) cot 7 d) tan (0 ). Determine the approximate value for each. Give answers to the nearest hundredth of a unit. a) sec. b) P θ. tan c) csc 7 d) sin 0.7. In which quadrant will θ terminate if angle θ is in standard position with the given conditions? a) cos θ < 0 b) sin θ > 0 c) cot θ > 0 d) cos θ > 0 and cot θ < 0 e) sin θ < 0 and sec θ > 0 f ) sec θ < 0 and tan θ < 0. Express each quantity as the same trigonometric ratio using its reference angle. For example cos 10 = cos 0. a) sin 0 b) cos 10 c) tan 100 d) csc 0 e) cot 00 f ) sec Determine the exact measure of all angles that satisfy the given conditions. a) tan θ = 1 domain 0 θ < 0 b) cosθ= domain 180 θ < 180 c) csc θ = domain 180 θ < 90 d) sin θ = 1 domain 0 θ < 0 8. Determine the exact measure of each angle. a) sin θ= domain 0 θ < b) sec θ = 1 domain θ < 1 c) cosθ= domain 0 θ < d) cot θ = 1 domain θ < 9. Determine the approximate measure of each angle. Use diagrams to show the number of possible solutions and the quadrants in which they lie. Then give answers to the nearest hundredth of a unit where possible. a) sin θ = 0. domain θ b) cot θ =.87 domain θ c) sec θ =.87 domain 0 θ < 180 d) tan θ = 1. domain 180 θ < The point D( 1) lies on the terminal arm of an angle θ in standard position. What is the exact value of each trigonometric ratio for θ? Section. Extra Practice 1. Solve for θ where 0 θ 0. a) cos θ 0. = 0 b) tan θ+ = 0 c) sin θ + 1 = d) sec θ =. Solve for x where 0 x. a) cos x 0. = 0 b) sin x = 0 c) (sin x 1)(tan x 1) = 0 d) cos x cos x + = 0

3 . Determine the exact roots for each trigonometric equation in the specified domain. c) d) a) sin x + sin x = x < 180 b) cos x cos x + 1 = 0 0 x < c) cos x sin x cos x = 0 x <. Solve each equation for 0 θ <. Give solutions to the nearest hundredth of a radian. a) tan θ =. b) cos θ = 0.19 c) sin θ = 0.91 d) cot θ = 1.. Verify that θ= are solutions to the equation sin θ 1 = 0.. Does cos θ = have a solution? Explain. 7. Solve each equation for 0 x rounding solutions to four decimal places.. a) b) quadrant I a) tan x + tan x 7 = 0 b) tan x tan x + = 0 c) tan x tan x = 0 8. The solution to cos θ = 1 in the domain 0 θ < is θ = 0. Write the general solution for the equation in which the domain is real numbers. c) d) 9. Write the general solution for the equation sin x (sin x + 1) = Write the general solution for the equation sin x + sin x = 0. Answers Section.1 quadrant I no quadrant 1. a) b) I quadrant IV. a) 1. b).19 c) 0.79 d) a) 1 b) 10 c) 1.7 d) 1. a) 18 b) 9 c) d) 1 1. a) b) c) a) subtract 0 b) subtract and use fractions to determine the exact value c) subtract using your calculator and then round your answer to the required accuracy 8. a) 7º ± (0º)n where n is a natural number b) ± n radians where n is a natural number c) (1 ± n) radians where n is a natural number

4 cm radians 9a) two solutions; b) two solutions: Section. 1. a) x + y = 1 b) x + y = c) x + y = 8.81 d) x + y = and ; When the coordinates are substituted into x + y = 1 the LHS equals the RHS..a) b) c) 11 d) a) b) (0 1) c) 1 d) 1. a) b) 1 c) (1 0) d) 1. a) b) 180 c) 1 d) 0 7. a) 0 b) c) d) a) 1 Section. 1. a) 1 b) 1 c) 1 d) 1 e) b) a) b) or f ) 1 1. a) 1 c) 1 d) 1 e) f ). a) 0. b) 0.8 c). d) a) 1. b) 0.7 c) 1.0 d) 0.8. a) II or III b) I or II c) I or III d) IV e) IV f ) II. a) sin 0 b) cos 0 c) tan 80 d) csc 80 e) cot 0 f ) sec a) 1 1 b) 0 0 c) 0 d) a) b) c) d) 7 c) three solutions: 81.8 d) three solutions: sin θ= 1 cos θ= 1 1 tan θ= Section cscθ= 1 1 secθ= cot θ= 1 1. a) 0 00 b) c) 0 10 d) a) b) c) d). a) b) 0 c). a) 1..9 b) c) d) LS RS LS RS sin θ 1 0 sin θ 1 0 = ( ) sin 1 = ( ) sin 1 = (1) 1 = ( 1) 1 = 0 = 0. No. Example: The range of the cosine function is []. Cosine is undefined for values that are outside of this range. 7. a) b) c) n n I 9. x =n + n 10. (1+ n) n I

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