Question

Unit 6: Periodic Functions and Trigonometry

Answer 1

Just took the quiz.
A. 145°
C. /
A. 250°
D. -.87,-0.5
A. Sqrt(3)/2

Answer 2

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

$= 90 + 55$
$= 145 \degree$

The correct answer is A.

QUESTION 2

First let us find the acute angle in the fourth quadrant.

This is given by
$\tan( \theta) = \frac{ \frac{1}{2} }{ \frac{ \sqrt{3} }{2} }$

This implies that,

$\tan( \theta) =\frac{1}{ \sqrt{3} }$

$\theta=arctan(\frac{1}{ \sqrt{3} })$
$\theta=30 \degree$

The angle in standard position
$=( 360 - \theta) \degree$
$= 330 \degree$

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
$- 110 \degree$

We either add or subtract 360°.

Since we want the to be between 0° and 360°, we have to add 360° to get,

$- 110 + 360 = 250 \degree$

The correct answer is A.

QUESTION 4

The acute angle that
$210 \degree$

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,

$\cos(210 \degree) = - \cos(30 \degree)$

$\sin(210 \degree) = - \sin(30 \degree)$

Using the special angles,

$\cos(210 \degree) = - \frac{ \sqrt{3} }{2}$

$\sin(210 \degree) = - \frac{1}{2}$

Or

$\cos(210 \degree) = - 0.87$

$\sin(210 \degree) = - 0.5$

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,

$\sin(120 \degree) = \sin(60 \degree)$

Using special angles, the exact value is,

$\sin(120 \degree) = \frac{\sqrt{3}}{2}$

The correct answer is A.