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WB1.4 - Unit Circle and Other Circles

Last updated over 5 years ago

8 questions

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Question 1

1.

Explain why the point (0.96,-0.26) cannot be on the unit circle.

Question 2

2.

The x-coordinate of point P on the unit circle is 0. If point P is the result of rotating the point (1,0) by θ radians counterclockwise about the origin, find three angles that could represent θ. (One of these three angles must be negative).

Question 3

3.

Does
Explain why or why not?

Question 4

4.

Use the image below to determine which of the following statements are true? (Be ready to explain your answers with justification.)
a. sin(A) > 1
b. tan (A) < 1
c. cos(A) < 1
d. sin(A) < sin(B)
e. cos(A) < cos(B)
f. tan(A) < tan(B)

Question 5

5.

For which of these angles is the cosine negative? Justify your reasoning.
a. -π/4
b. -π/3
c. -2π/3
d. -4π/3
e. -11π/6

Question 6

6.

In what quadrant(s) are both sine and tangent negative? When are they different signs? Justify your reasoning.

Question 7

7.

The center of a Ferris wheel is 100 feet off the ground and its radius is 85 feet. You enter at the bottom of the Ferris wheel. If the Ferris wheel rotates 5π/4 radians from where you entered, how far are you above the ground? Round to the nearest foot. Hint: draw an image.

Question 8

8.

An analog clock reads 3:00pm, as shown in the image. Which of the following statements are true? Justify your reasoning.
a. In the next hour, the minute hand moves through an angle of 2π radians.
b. In the next 5 minutes, the minute hand will move through an angle of -π/6 radians.
c. After the minute hand movies through an angle of -π radians, is it 3:30pm?
d. When the hour hand moves through an angle of -π/6 radians, is it 4:00pm?
e. The angle the minute hand moves through is 12 times the angle the hour hand moves through.