1. What quadrant would the terminal side of the angle of t=4pie/3 be?
2. What quadrant would the terminal side of the angle of t=3pie/2
Print out the "trig wheel" on this page, it will come in handy
http://ll043.k12.sd.us/slides/trigonometry.htm
To determine the quadrant of an angle, you need to consider its reference angle and the signs of the coordinates within each quadrant on the Cartesian plane.
1. To find the quadrant of the angle with t = 4π/3:
a) Start by converting the angle to its reference angle, which is the acute angle formed between the terminal side and the x-axis.
The reference angle for t = 4π/3 is π/3 since it is the angle within 0 to π/2.
b) Since the reference angle of π/3 lies within the first quadrant (where both x and y coordinates are positive), the terminal side of the angle t = 4π/3 would also lie within the first quadrant.
2. To find the quadrant of the angle with t = 3π/2:
a) Convert the angle to its reference angle, which is the acute angle formed between the terminal side and the x-axis.
The reference angle for t = 3π/2 is π/2 since it is the angle within 0 to π/2.
b) In the plane, the angle with the reference angle of π/2 is located on the y-axis, which means its terminal side would intersect either the positive y-axis or the negative y-axis.
Since the y-coordinate is positive in the second quadrant and negative in the third quadrant, the terminal side of the angle t = 3π/2 would lie in the second quadrant.
Remember, understanding the reference angle and the signs of the coordinates in each quadrant will help determine the correct quadrant of an angle.