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nekit [7.7K]
3 years ago
11

Unit 6: Periodic Functions and Trigonometry

Mathematics
2 answers:
Ne4ueva [31]3 years ago
8 0
Just took the quiz.
A. 145°
C. /
A. 250°
D. -.87,-0.5
A. Sqrt(3)/2
prisoha [69]3 years ago
5 0
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.
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