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Hotmath Practice Problems

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Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:TrigonometrySection:The Unit Circle
 

Problem: 1

Find sin θ, cos θ, and tan θ if θ is the angle between the x–axis and the ray , where O is the origin and the point P is located on the unit circle.


Problem: 3

Find sin θ, cos θ, and tan θ if θ is the angle between the x–axis and the ray , where O is the origin and the point P(0, 1) is located on the unit circle.


Problem: 5

In the given figure, find the exact coordinates of the intersection of the unit circle and the terminal side of the angle.


Problem: 7

Evaluate the values of the six trigonometric functions for some radian measure s, where s is the distance between the points A (1, 0) and P (12/13, –5/13) along the unit circle

x2 + y2 = 1.


Problem: 9

Evaluate the values of the six trigonometric functions for some number s, where s is the distance between the points A (1, 0) and

along the unit circle x2 + y2 = 1.


Problem: 11

Sketch an angle of –45 in standard position. Then find the exact values of the cosine and the sine of –45 using a right triangle.


Problem: 13

Evaluate the values of the six trigonometric functions for 4π/3.


Problem: 15

Verify the identity cos2 x + sin2 x = 1 for a) x = 6π/5 and b) x = 0.4 (both values in radians.)


Problem: 1

Find sin θ, cos θ, and tan θ if θis the angle between the x–axis and the ray , where O is the origin and the point P is located on the unit circle.


Problem: 3

Find sin θ, cos θ, and tan θ if θ is the angle between the x–axis and the ray , where O is the origin and the point P(0, 1) is located on the unit circle.


Problem: 5

In the given figure, find the exact coordinates of the intersection of the unit circle and the terminal side of the angle.


Problem: 7

Evaluate the values of the six trigonometric functions for some radian measure s, where s is the distance between the points A (1, 0) and P (12/13, –5/13) along the unit circle

x2 + y2 = 1.


Problem: 9

Evaluate the values of the six trigonometric functions for some number s, where s is the distance between the points A (1, 0) and

along the unit circle x2 + y2 = 1.


Problem: 11

Sketch an angle of –45 in standard position. Then find the exact values of the cosine and the sine of –45 using a right triangle.


Problem: 13

Evaluate the values of the six trigonometric functions for 4π/3.


Problem: 15

Verify the identity cos2 x + sin2 x = 1 for a) x = 6π/5 and b) x = 0.4 (both values in radians.)