Final answer:
Two positive coterminal angles with 5pi/4 are 13pi/4 and 21pi/4, while two negative angles are -3pi/4 and -11pi/4. These angles are found by adding or subtracting multiples of 2pi to the original angle.
Step-by-step explanation:
To find two positive angles and two negative angles that are coterminal with the given angle of 5pi/4, we need to add and subtract multiples of 2pi radians (the angle of one full rotation in radians).
For positive coterminal angles, you can use the following formula:
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- Positive Angle 1 = 5pi/4 + 2pi = 13pi/4
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- Positive Angle 2 = 5pi/4 + 2(2pi) = 21pi/4
For negative coterminal angles, use this formula:
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- Negative Angle 1 = 5pi/4 - 2pi = -3pi/4
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- Negative Angle 2 = 5pi/4 - 2(2pi) = -11pi/4
This way, we find the angles 13pi/4 and 21pi/4 as positive coterminal angles and -3pi/4 and -11pi/4 as negative coterminal angles with 5pi/4.