MATH Basic Algebra II  - Unit 30: Circular Trigonometry

Angle Measurement


1) An angle with its vertex at the origin and its initial side along the positive x-axis is said to be in what position?1

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2)

An angle rotating clockwise has what kind of a measure? 


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3)

Two different angles having the same terminal side are called what? 


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4)

Determine all the coterminal angles. 


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5)

Determine all the coterminal angles.


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Reference Angles


6)

Determine the reference angle for the given angle.


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7)

Determine the reference angle for the given angle.


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8)

Determine the reference angle for the given angle.


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9)

Determine the reference angle for the given angle.


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Degree and Radian Measure

In the following problems, convert the degree measures to radians. To enter a radian measure via the keyboard, express the answer in the same format as the sample answer shown below.

10)

What is the radian measure of an angle of 27º ?


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11)

What is the radian measure for 150º ?


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12)

What is the radian measure for  –40º?


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13)

What is the radian measure for 260°?


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In the following problems, convert the radian measures to degrees. To enter a degree measure via the keyboard, express the answer in the same format as the sample answer shown below.


14)

Solve.


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15)

Solve.


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16)

Solve.


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17)

Solve.


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Right Triangles in Quadrant 1

To enter a square root via the keyboard, express the answer in the same format as the sample answer shown below.


trigonometric ratios


18)

Evaluate the trigonometric ratio.


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19)

Evaluate the trigonometric ratio.


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20)

Evaluate the trigonometric ratio.


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 Right Triangles and Reference Angles in Quadrants #2, 3, 4


21)

Evaluate the trigonometric ratio. 


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22)

Evaluate the trigonometric ratio. 


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23)

Evaluate the trigonometric ratio.


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trigonometric ratios


24)

Evaluate the trigonometric ratio.


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25)

Evaluate the trigonometric ratio.


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26)

Evaluate the trigonometric ratio.


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trigonometric ratio


27)

Evaluate the trigonometric ratio.


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28)

Evaluate the trigonometric ratio.


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29)

Evaluate the trigonometric ratio.


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trigonometric ratios


30)

Evaluate the trigonometric ratio.


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31)

Evaluate the trigonometric ratio.


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32)

Evaluate the trigonometric ratio.


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trigonometric ratios


33)

Evaluate the trigonometric ratio.


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34)

Evaluate the trigonometric ratio.


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35)

Evaluate the trigonometric ratio.


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trigonometric ratios


36)

Evaluate the trigonometric ratio.


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37)

Evaluate the trigonometric ratio.


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38)

Evaluate the trigonometric ratio.


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Trigonometric Ratios for Quadrantal Angles

In the following problems, find the exact values of the trigonometric ratios for 2pi on the unit circle.


39)

Evaluate the trigonometric ratio.


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40)

Evaluate the trigonometric ratio.


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41)

Evaluate the trigonometric ratio.


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trigonometric ratios


42)

Evaluate the trigonometric ratio.


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43)

Evaluate the trigonometric ratio.


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44)

Evaluate the trigonometric ratio.


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In the following problems, find the exact values of the trigonometric ratios for 0 on the unit circle.


45)

Evaluate the trigonometric ratio.

sin 0


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46)

Evaluate the trigonometric ratio.

cos 0


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47)

Evaluate the trigonometric ratio.

tan 0


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trigonometric ratios


48)

Evaluate the trigonometric ratio.


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49)

Evaluate the trigonometric ratio.


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50)

Evaluate the trigonometric ratio.


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51) Extended Learning

Watch the following video, then write a five-sentence paragraph summarizing the video.


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