1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
Answer:
From given options, -180 is not a coterminal angle of 120 degrees
Solution:
Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Coterminal angles of 120 degrees are:
120 degrees + 360 degrees = 480 degrees
120 degrees - 360 degrees = 240 degrees
720 degrees + 120 degrees = 840 degrees
120 degrees - 720 degrees = -600 degrees
Therefore:
Positive Angle 1 (Degrees) 480
Positive Angle 2 (Degrees) 840
Negative Angle 1 (Degrees) -240
Negative Angle 2 (Degrees) -600
Therefore from given options, -180 is not a coterminal angle of 120 degrees
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90
A. Cos theta = undefined
B. Sin theta = -1
C. Tan theta = 0
Answer:
Sin theta = -1 is correct
Solution:
given angle is -90
Find the reference angle for -90
Reference angle = 360 - 90 = 270 degrees
Unit circle diagram is attached below
And from the unit circle, we know the coordinates for 270 degrees are (0, -1)
Our angle - 90 degrees lies in (0, -1)
Unit circle coordinates are given by [tex](cos \theta , sin \theta )[/tex]
This means,
cos (-90 ) = 0 and sin(-90) = -1
We know that,
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
[tex]tan \theta = \frac{-1}{0}[/tex] = undefined
Therefore from options, sin theta = -1 is correct
