3. Unit Circle

Defining the Unit Circle

3. Unit Circle

# Defining the Unit Circle - Video Tutorials & Practice Problems

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## Introduction to the Unit Circle

Video duration:

6mPlay a video:

2

Problem

ProblemIdentify the quadrant that the given angle is located in.

$\frac{7\pi}{4}$ radians

A

Quadrant I

B

Quadrant II

C

Quadrant III

D

Quadrant IV

3

Problem

ProblemIdentify the quadrant that the given angle is located in.

$\frac{\pi}{7}$ radians

A

Quadrant I

B

Quadrant II

C

Quadrant III

D

Quadrant IV

4

Problem

ProblemIdentify the quadrant that the given angle is located in.

$\frac{2\pi}{3}$ radians

A

Quadrant I

B

Quadrant II

C

Quadrant III

D

Quadrant IV

5

Problem

ProblemIdentify the quadrant that the given angle is located in.

$\frac{6\pi}{5}$ radians

A

Quadrant I

B

Quadrant II

C

Quadrant III

D

Quadrant IV

6

Problem

ProblemTest whether the point is on the unit circle by plugging it into the equation, $x^2+y^2=1$.

$\left(\frac{-\sqrt2}{2},\frac{-\sqrt2}{2}\right)$

A

On Unit Circle

B

NOT on Unit Circle

C

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PRACTICE PROBLEMS AND ACTIVITIES (88)

- In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the value...
- Use the formula ω = θ/t to find the value of the missing variable.ω = 2π/3 radians per sec, t = 3 sec
- Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.s = π/2
- Use the formula ω = θ/t to find the value of the missing variable.ω = 0.91 radian per min, t = 8.1 min
- Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.s = 2π
- Use the formula ω = θ/t to find the value of the missing variable.θ = 3π/4 radians, t = 8 sec
- Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.s = ―π
- Use the formula ω = θ/t to find the value of the missing variable.θ = 3.871 radians, t = 21.47 sec
- Find each exact function value. See Example 2. ...
- Use the formula ω = θ/t to find the value of the missing variable.θ = 2π/9 radian , ω = 5π/27 radian per min
- Find each exact function value. See Example 2.tan 3π/4
- Use the formula v = r ω to find the value of the missing variable.r = 12 m , ω = 2π/3 radians per sec
- Find each exact function value. See Example 2.csc 11π/6
- Use the formula v = r ω to find the value of the missing variable.v = 9 m per sec , r = 5 m
- Find each exact function value. See Example 2. ...
- Use the formula v = r ω to find the value of the missing variable.v = 12 m per sec, ω = 3π/2 radians per sec
- Find each exact function value. See Example 2.cos 7π/4
- The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the form...
- Find each exact function value. See Example 2.sin (4π/3)
- The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the form...
- Find each exact function value. See Example 2.sec 23π/6
- The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the form...
- Find each exact function value. See Example 2.tan 5π/6
- Find a calculator approximation to four decimal places for each circular function value. See Example 3. ...
- Find a calculator approximation to four decimal places for each circular function value. See Example 3. ...
- Find each exact function value.tan π/3
- Find the angular speed ω for each of the following.a gear revolving 300 times per min
- Find the angular speed ω for each of the following.a wind turbine with blades turning at a rate of 15 revoluti...
- Find a calculator approximation to four decimal places for each circular function value. See Example 3. ...
- Find each exact function value.sin ( ―5π/6)
- Find the linear speed v for each of the following.the tip of the minute hand of a clock, if the hand is 7 cm...
- Find each exact function value.csc ( ―11π/6)
- Find the linear speed v for each of the following.a point on the edge of a flywheel of radius 2 m, rotating 42...
- Without using a calculator, determine which of the two values is greater.tan 1 or tan 2
- Find the linear speed v for each of the following.the tip of a propeller 3 m long, rotating 500 times per min ...
- Without using a calculator, determine which of the two values is greater. cos 2 or sin 2
- Find the linear speed v for each of the following.a point on the equator moving due to Earth's rotation, if th...
- Find a calculator approximation to four decimal places for each circular function value.sin 1.0472
- Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)
- Find a calculator approximation to four decimal places for each circular function value.sec 7.3159
- Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement tr...
- A thread is being pulled off a spool at the rate of 59.4 cm per sec. Find the radius of the spool if it makes ...
- Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement tr...
- The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. ...
- Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the ra...
- Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement tr...
- Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the ra...
- Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the ra...
- Find the exact value of s in the given interval that has the given circular function value.[ 0, π/2] ; cos s =...
- Find the exact value of s in the given interval that has the given circular function value.[ π , 3π/2] ; sec s...
- Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement t...
- Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement t...
- Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement ...
- Find the exact value of s in the given interval that has the given circular function value.[π/2, π] ; sin s = ...
- Find the exact value of s in the given interval that has the given circular function value.[π, 3π/2] ; tan s =...
- Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluat...
- Find the exact value of s in the given interval that has the given circular function value.[3π/2, 2π] ; tan s ...
- Find the exact values of s in the given interval that satisfy the given condition.[0, 2π) ; sin s = -√3 / 2
- Find the exact values of s in the given interval that satisfy the given condition.[0 , 2π) ; cos² s = 1/2
- Find the exact values of s in the given interval that satisfy the given condition.[-2π , π) ; 3 tan² s = 1
- Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating a...
- For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which qua...
- For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which qua...
- Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluat...
- In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the value...
- In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, �...
- In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, �...
- In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, �...
- In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric fu...
- In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric fu...
- In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 to find the value of the trigonometric fu...
- In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, �...
- In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, �...
- In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, �...