1.Observe the given circle on the points corresponding to 0, 30, 45, and 60 degr

Question

1.Observe the given circle on the points corresponding to 0, 30, 45, and 60 degrees are given.

2. Complete the unit circle by filling in the remaining coordinates which correspond to (reference) special angles. This should be done without the use of a calculator, and all values should be left as integers or rationalized fractions. Using the completed unit circle, answer the following:

1. sin 5/4=

2. cos 5/6=

Using your knowledge of coterminal angles, answer the following:

3. cos (-30°)=

4. sin 405°=

5. Any given angle is associated with an infinite number of coterminal angles. List four angles IN RADIAN MEASURE that are coterminal to 90°.

2' 2 2'2 3T 33 4120 90° 60045,4 5n 2,2 135 6150° 30 6 0° 0 360° 2 (1,0) »-t-180° 3300 315 11 210° 7m," 225 ( , ) b5m, 240° 2700 300°X76 4 3

Explanation / Answer

2pi/3 = -1/2 , sqrt 3/2

3pi/4 = -sqrt 2 / 2 , sqrt 2/2

5pi/6 = - sqrt 3/2 , 1/2

pi = -1 , 0

7pi/6 = -5pi/6 = (-sqrt 3/2 , -1/2 )

5pi/4 = -3pi/4 = (-sqrt 2/2 , -sqrt 2 /2 )

4pi/3 = -2pi/3 = (-1/2 , - sqrt 3/2 )

3pi/2 = -pi/2 = (0,-1)

5pi/3 = -pi/3 = (1/2 , -sqrt 3/2 )

7pi/4 = -pi/4 = (sqrt 2/2 , - sqrt 2/2 )

11pi/6 = -pi/6 = ( sqrt 3/2 , -1/2 )

1) sin 5pi/4 = - sqrt 2/2

2) cos 5pi/6 = - sqrt 3/2

3) cos (-30) = sqrt 3/2

4) sin (405) = sin 45 = sqrt 2 / 2

5) coterminal angles with 90 =pi/2 - 2pi = -3pi/2

pi/2 + 2pi =5pi/2

pi/2 + 4pi = 9pi/2

pi/2 - 2pi = -7pi/2

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