Unit Circle Practice Quiz

Created by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Sophia Smith
Sophia Smith, Quiz Creator
Sophia is a skilled quiz creator at ProProfs.com, known for her engaging and innovative quizzes. Her enthusiasm for learning and creativity results in quizzes that are both fun and educational. Sophia's dedication to excellence ensures that users always have a top-notch experience with her interactive content.
Quizzes Created: 1083 | Total Attempts: 3,548,751
| Attempts: 1,367
Quiz Flashcard
SettingsSettings
Please wait...
  • 1/10 Questions

    In Calculus, almost all the references to the trigonometric functions are based on the unit circle.

    • True
    • False
Please wait...
About This Quiz

A unit circle is defined as a circle with a unit radius. Take this unit circle quiz and test your knowledge about this important concept of trigonometry in math. The unit circle is mainly used to learn and talk about lengths and angles. If you understand this concept of circles, it is going to be an interesting quiz for you. Give this easy quiz a try and see what score you get! All the best! You can share the quiz with other math lovers also.

Unit Circle Practice Quiz - Quiz

Quiz Preview

  • 2. 

    The Unit Circle is a circle with its center at

    • Origin (0,0)

    • (0,1)

    • (1,0)

    • (1,1)

    Correct Answer
    A. Origin (0,0)
    Explanation
    The Unit Circle is a circle with its center at the origin (0,0) because in the coordinate plane, the origin represents the point where the x-axis and y-axis intersect. Since the Unit Circle is used to represent angles and distances in trigonometry, it makes sense for it to be centered at the origin. This allows for easy calculations and comparisons of trigonometric functions for various angles.

    Rate this question:

  • 3. 

    What is the value of 2π/3?

    • 90 degrees 

    • 100 degrees

    • 120 degrees

    • 150 degrees

    Correct Answer
    A. 120 degrees
    Explanation
    The value of 2π/3 is equal to 120 degrees. This is because a full circle is equal to 360 degrees, and 2π radians is equal to 360 degrees. Therefore, to find the value in degrees, we can set up a proportion: 2π/3 = 360/x. Solving for x, we find that x is equal to 120 degrees.

    Rate this question:

  • 4. 

    What are the properties of a unit circle?

    • Circle whose center is at the origin

    • Circle whose radius is one

    • The circumference of the unit circle is 2Π

    • All of the above

    Correct Answer
    A. All of the above
    Explanation
    The properties of a unit circle include having its center at the origin, having a radius of one, and having a circumference of 2π. Therefore, the correct answer is "All of the above."

    Rate this question:

  • 5. 

    What is the radius of a unit circle?

    • 1

    • 2

    • 3

    • 4

    Correct Answer
    A. 1
    Explanation
    The radius of a unit circle is always 1. A unit circle is defined as a circle with a radius of 1 unit. It is a special circle used in mathematics to simplify calculations and understand geometric properties. The radius is the distance from the center of the circle to any point on its circumference, and in the case of a unit circle, this distance is always 1 unit.

    Rate this question:

  • 6. 

    What is the value of π/3?

    • 30 degrees

    • 60 degrees

    • 90 degrees

    • 180 degrees

    Correct Answer
    A. 60 degrees
    Explanation
    The value of π/3 is equal to 60 degrees. This is because π radians is equivalent to 180 degrees, so to find the value of π/3 in degrees, we divide 180 by 3, resulting in 60 degrees.

    Rate this question:

  • 7. 

    What is the formula for a unit circle?

    • X+y=1

    • X2+y2=1

    • X3+y3=1

    • None of the above

    Correct Answer
    A. X2+y2=1
    Explanation
    The formula for a unit circle is x2+y2=1. This equation represents all the points on a circle with a radius of 1, centered at the origin (0,0) in a coordinate plane. It states that the square of the x-coordinate plus the square of the y-coordinate equals 1. This equation is derived from the Pythagorean theorem and is fundamental in trigonometry and geometry.

    Rate this question:

  • 8. 

    What is 2 radians on a unit circle?

    • 90 degrees

    • 180 degrees

    • 270 degrees

    • 360 degrees

    Correct Answer
    A. 360 degrees
    Explanation
    2 radians on a unit circle is equivalent to 360 degrees. A unit circle has a radius of 1, and a full rotation around the circle is equal to 2π radians or 360 degrees. Since 2 radians is the same as a full rotation, the answer is 360 degrees.

    Rate this question:

  • 9. 

    What is the area of a unit circle?

    • A = 2πr

    • A = πr2

    • A = π2r

    • A = πr/2

    Correct Answer
    A. A = πr2
    Explanation
    The area of a unit circle is given by the formula A = πr^2, where r is the radius of the circle. In this case, the radius is 1 (since it's a unit circle), so the area is A = π(1)^2 = π. Therefore, the correct answer is A = πr^2.

    Rate this question:

  • 10. 

    What is the value of sin of 1 unit circle? (in rad)

    • 0.7414709828

    • 0.8414709848

    • 0.8417709848

    • 0.9464709848

    Correct Answer
    A. 0.8414709848
    Explanation
    The value of sin(1) on the unit circle is approximately 0.8414709848. This can be determined by calculating the y-coordinate of the point on the unit circle that corresponds to an angle of 1 radian. Since the unit circle has a radius of 1, the y-coordinate represents the sine of the angle.

    Rate this question:

Quiz Review Timeline (Updated): Mar 29, 2023 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 29, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 12, 2023
    Quiz Created by
    Sophia Smith
Back to Top Back to top
Advertisement
×

Wait!
Here's an interesting quiz for you.

We have other quizzes matching your interest.