__Questions 1:__

Graph - 435^{o} in standard position.

__Solution to Question 1:__

- 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

__Questions 2:__

Graph 9 Pi / 4 in standard position.

__Solution to Question 2:__

- 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.

__Questions 3:__

In which quadrant is the terminal side of an angle of - 3 Pi / 4 located?

__Solution to Question 3:__

- The terminal side of - 3 Pi / 4 is located in quadrant three.

__Questions 4:__

In which quadrant is the terminal side of an angle of 750^{o} located?

__Solution to Question 4:__

- 750 degrees = 360 degrees + 360 degrees + 30 degrees. Hence an angle of 750 degrees, in standard position, has its terminal side in quadrant one.

__Questions 5:__

Find a coterminal angle t to angle - 27 Pi / 12 such that 0 <= t < 2 Pi.

__Solution to Question 5:__

- 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..

__Questions 6:__

Find an angle t that is coterminal to 560^{o} such that 0 <= t < 360^{o}.

__Solution to Question 6:__

- 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.

__Questions 7:__

Determine the complementary angle t to Pi / 12.

__Solution to Question 7:__

- The complementary angle to Pi / 12 is obtained as follows

t = Pi / 2 - Pi / 12 = 5 Pi / 12

__Questions 8:__

Determine the complementary angle t to 34^{o}.

__Solution to Question 8:__

- The complementary angle t to 34 degrees is given by

t = 90 degrees - 34 degrees = 56 degrees.

__Questions 9:__

Determine the supplementary angle t to 96^{o}.

__Solution to Question 9:__

- The supplementary angle t to 96 degrees is give by

t = 180 degrees - 96 degrees = 84 degrees.

__Questions 10:__

Convert 75^{o} to radians .

__Solution to Question 10:__

- 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)

__Questions 11:__

Convert 7 Pi / 4 to degrees .

__Solution to Question 11:__

- 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.

__Questions 12:__

Convert 1.5 radians to degrees.

__Solution to Question 12:__

- 1.5 radians into degrees is given by

1.5 * 180 / Pi = 85.94 degrees (rounded to 2 decimal places)

__Questions 13:__

Convert 61^{o} 05' 12" to degrees in decimal form.

__Solution to Question 13:__

- 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).

__Questions 14:__

A central angle t of a circle with radius 2 meters subtends an arc of length 1.5 meters. Find angle t in degrees.

__Solution to Question 14:__

- 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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