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Hotmath Practice Problems

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Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:Trigonometric Identities, Graphs and FormulasSection:Circular Functions, Periodicity and Symmetry
 

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

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


Problem: 5

Evaluate the values of the six trigonometric functions for some number s, where s is the distance (in radians) between the points A (1, 0) and P (12/13, –5/13) along the unit circle x2 + y2 = 1


Problem: 7

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

along the unit circle x2 + y2 = 1.


Problem: 9

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: 11

Find an angle that is coterminal with a 405 angle and which lies between 0 and 360 .


Problem: 13

Find an angle that is coterminal with a –234 angle and which lies between 0 and 360 .


Problem: 15

Find a negative and positive angle that is coterminal with the 75 angle.


Problem: 17

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


Problem: 19

Find the value of x where


Problem: 21

Check whether the identity cos2 x + sin2 x = 1 is true for x = 6π/5.


Problem: 23

Check whether the identity cos2 x + sin2 x = 1 is true for x = 0.4.


Problem: 25

Plot the graph of the function f in the interval –4 x 4 and state whether the function f is odd or even in that interval. The function has a period p = 2.


Problem: 27

Find out whether the function f(x) = x3 + 2x is even, odd, or neither the both.


Problem: 29

Find out whether the function f(x) = 3x sin x + 4 is even, odd, or neither the both.


Problem: 31

For the given function, find the period and the amplitude.


Problem: 35

Find the period, the maximum, and the minimum for the given function.


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

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


Problem: 5

Evaluate the values of the six trigonometric functions for some number s, where s is the distance (in radians) between the points A (1, 0) and P (12/13, –5/13) along the unit circle x2 + y2 = 1


Problem: 7

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

along the unit circle x2 + y2 = 1.


Problem: 9

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: 11

Find an angle that is coterminal with a 405 angle and which lies between 0 and 360.


Problem: 13

Find an angle that is coterminal with a –234 angle and which lies between 0 and 360.


Problem: 15

Find a negative and positive angle that is coterminal with the 75 angle.


Problem: 17

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


Problem: 19

Find the value of x where


Problem: 21

Check whether the identity cos2 x + sin2 x = 1 is true for x = 6π/5.


Problem: 23

Check whether the identity cos2 x + sin2 x = 1 is true for x = 0.4.


Problem: 25

Plot the graph of the function f in the interval –4 x 4 and state whether the function f is odd or even in that interval. The function has a period p = 2.


Problem: 27

Find out whether the function f(x) = x3 + 2x is even, odd, or neither the both.


Problem: 29

Find out whether the function f(x) = 3x sin x + 4 is even, odd, or neither the both.


Problem: 31

For the given function, find the period and the amplitude.


Problem: 35

Find the period, the maximum, and the minimum for the given function.