QUESTION 1
For this first question, we need to measure the angle from the positive x-axis up to the terminal side, which is in the second quadrant.
The measure of the angle
[tex] = 90 + 55[/tex]
[tex] = 145 \degree[/tex]
The correct answer is A.
QUESTION 2
First let us find the acute angle in the fourth quadrant.
This is given by
[tex] \tan( \theta) = \frac{ \frac{1}{2} }{ \frac{ \sqrt{3} }{2} } [/tex]
This implies that,
[tex] \tan( \theta) =\frac{1}{ \sqrt{3} }[/tex]
[tex] \theta=arctan(\frac{1}{ \sqrt{3} })[/tex]
[tex] \theta=30 \degree[/tex]
The angle in standard position
[tex] =( 360 - \theta) \degree[/tex]
[tex] = 330 \degree[/tex]
We measure from the positive x-axis in the anticlockwise direction.
The correct answer is B.
QUESTION 3
Coterminal angles are angles in standard position that have the same terminal side.
To find angles that are coterminal with
[tex] - 110 \degree[/tex]
We either add or subtract 360°.
Since we want the to be between 0° and 360°, we have to add 360° to get,
[tex] - 110 + 360 = 250 \degree[/tex]
The correct answer is A.
QUESTION 4
The acute angle that
[tex]210 \degree[/tex]
makes with the x-axis is 30°.
Since 210 is in the third quadrant, both the sine and cosine ratio are negative.
This implies that,
[tex] \cos(210 \degree) = - \cos(30 \degree) [/tex]
[tex] \sin(210 \degree) = - \sin(30 \degree) [/tex]
Using the special angles,
[tex] \cos(210 \degree) = - \frac{ \sqrt{3} }{2} [/tex]
[tex] \sin(210 \degree) = - \frac{1}{2} [/tex]
Or
[tex] \cos(210 \degree) = - 0.87[/tex]
[tex] \sin(210 \degree) = - 0.5[/tex]
The correct answer is D.
QUESTION 5
The acute angle that 120° makes with the x-axis is 60°.
Since 120° is in the second quadrant, the sine ratio is positive.
This implies that,
[tex] \sin(120 \degree) = \sin(60 \degree) [/tex]
Using special angles, the exact value is,
[tex] \sin(120 \degree) = \frac{\sqrt{3}}{2} [/tex]
The correct answer is A.
