Explanation Given information: The unit circle is Explanation: Let P ( x , y ) be the point on the unit circle that corresponds to the angle θ . By using definition of trigonometric functions, sin θ = y , cos θ = x . The angle π 3 and the angle B lies on the same line. The measure of an angle B from the x − axis is π 3 + π = 4 π 3 Since the angle between the π 3 and the B is π ; therefore, the measure of the angle B is 4 π 3 Similarly, The angle π 4 and the angle C lie on the same line. The measure of an angle C from the x − axis is π 4 + π = 5 π 4 Therefore, the measure of an angle C is 5 π 4 . The angle π 6 and the angle D lie on the same line. The measure of an angle D from the x − axis is π 6 + π = 7 π 6 Therefore, the measure of an angle D is 7 π 6 The angle 0 and the angle E lie on the same line. The measure of an angle E from the x − axis is 0 + π = π Therefore, the measure of an angle E is π . The angle 11 π 6 and the angle F lie on the same line. The measure of an angle F from the x − axis is 11 π 6 − π = 5 π 6 Therefore, the measure of an angle F is 5 π 6 The angle 7 π 4 and the angle G lie on the same line. The measure of an angle G from the x − axis is 7 π 4 − π = 3 π 4 Therefore, the measure of an angle G is 3 π 4 . The angle 5 π 3 and the angle H lie on the same line. The measure of an angle H from the x − axis is 5 π 3 − π = 2 π 3 Therefore, the measure of an angle H is 2 π 3 The measure of angle I is π 2 The angle A and the angle I lie on the same line. The measure of an angle A from the x − axis is π 2 + π = 3 π 2 Therefore, the measure of an angle A is 3 π 2 i) When θ = 0 , sin 0 = 0 , cos 0 = 1 Thus, the point P is ( 1 , 0 ) Therefore, the point corresponding to the angle 0 is ( 1 , 0 ) ii) When θ = π 6 , sin π 6 = 1 2 , cos π 6 = 3 2 Thus, the point P is ( 3 2 , 1 2 ) Therefore, the point corresponding to the angle π 6 is ( 3 2 , 1 2 ) iii) When θ = π 4 , sin π 4 = 2 2 , cos π 4 = 2 2 Thus, the point P is ( 2 2 , 2 2 ) Therefore, the point corresponding to the angle π 4 is ( 2 2 , 2 2 ) iv)When θ = π 3

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Author: Michael Sullivan

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Chapter 6, Problem 55RE

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Chapter 6, Problem 54RE

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The missing angles and the corresponding points P on the given unit circle,

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