Trigonometry questions related to angles in standard position, coterminal angles, complementary and supplementary angles, as well conversion from degrees to radians and vice versa, are presented. The solutions and answers are provided.

## Question 1Graph - 435^{o} in standard position.
- Start from the initial side on the horizontal axis, positive direction, rotate 435 degrees in the negative direction to locate the terminal side which is in quadrant four. It helps to note that 435 degrees = 360 degrees + 75 degrees
## Question 2Graph 9 Pi / 4 in standard position.
- Start from the initial side on the horizontal axis, positive direction, rotate 9 Pi / 4 (radians) in the positive direction to locate the terminal side which is in quadrant one. Note that 9 Pi / 4 = 2 Pi + Pi / 4.
## Question 3In which quadrant is the terminal side of an angle of - 3 Pi / 4 located?
- The terminal side of - 3 Pi / 4 is located in quadrant three.
## Question 4In which quadrant is the terminal side of an angle of 750^{o} located?
- 750 degrees = 360 degrees + 360 degrees + 30 degrees. Hence an angle of 750 degrees, in standard position, has its terminal side in quadrant one.
## Question 5Find a coterminal angle t to angle - 27 Pi / 12 such that 0 <= t < 2 Pi.
- We first note that - 27 Pi / 12 = -24 Pi / 12 - 3 Pi / 4 = - 2 Pi - 3 Pi / 4. A coterminal angle is obtained by adding or subtracting a whole number of 2 Pi (or 360 degrees). Hence a positive coterminal angle to - 27 Pi / 12 may be obtained by adding 2 (2 Pi) = 4 Pi.
t = - 27 Pi / 12 + 4 Pi = 7 Pi / 4
- Note that t is positive and smaller than 2 Pi..
## Question 6Find an angle t that is coterminal to 560^{o} such that 0 <= t < 360^{o}.
- Note that 560 degrees = 360 degrees + 200 degrees which is greater than 360 degrees. So to obtain a coterminal angle smaller than 360 degrees we need to subtract 360 degrees from 560 degrees.
t = 560 degrees - 360 degrees = 200 degrees.
## Question 7Determine the complementary angle t to Pi / 12.
- The complementary angle to Pi / 12 is obtained as follows
t = Pi / 2 - Pi / 12 = 5 Pi / 12
## Question 8Determine the complementary angle t to 34^{o}.
- The complementary angle t to 34 degrees is given by
t = 90 degrees - 34 degrees = 56 degrees.
## Question 9Determine the supplementary angle t to 96^{o}.
- The supplementary angle t to 96 degrees is give by
t = 180 degrees - 96 degrees = 84 degrees.
## Question 10Convert 75^{o} to radians .
- To convert from degrees to radians, we multiply by Pi and divide by 180. Hence 75 degrees in radians is given by
75 * Pi / 180 = 5 Pi / 12 = 1.31 (rounded to 2 decimal places)
## Question 11Convert 7 Pi / 4 to degrees .
- To convert from radians to degrees, we multiply by 180 and divide by Pi. Hence 7 Pi / 4 in degrees is given by
(7 Pi / 4) * 180 / Pi
- which simplifies to
= 315 degrees.
## Question 12Convert 1.5 radians to degrees.
- 1.5 radians into degrees is given by
1.5 * 180 / Pi = 85.94 degrees (rounded to 2 decimal places)
## Question 13Convert 61^{o} 05' 12" to degrees in decimal form.
- An angle of 61 degrees 5 minutes and 12 seconds in decimal form is given by
61 + 5 / 60 + 12 / 3600 = 61.07 (rounded to 2 decimal places).
## Question 14A central angle t of a circle with radius 2 meters subtends an arc of length 1.5 meters. Find angle t in degrees.
- The use of the arc length formula s = r t where t is the angle (in radians) that subtends an arc of length s gives
1.5 = 2 t
- Solve for t to obtain
t = 1.5 / 2 = 0.75 (radians)
- We now convert t in degrees
t = 0.75 * 180 / Pi = 42.97 degrees (rounded to 2 decimal places)
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