Trigonometry: Unit Circle Basics
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Questions and Answers

What are the points on the unit circle?

  • (Cot, Csc)
  • (Cos, Tan) (correct)
  • (Sin, Cos)
  • (Tan, Sec)

    • What is Cos $\frac{\pi}{3}$?

    1/2

    What is Cos $\frac{2\pi}{3}$?

    -1/2

    What is Sin $\frac{2\pi}{3}$?

    <p>3/2</p> Signup and view all the answers

    What quadrant is $\frac{5\pi}{3}$ in?

    <p>Fourth</p> Signup and view all the answers

    In quadrant 4, what unit is positive?

    <p>Cosine</p> Signup and view all the answers

    Name the four focus points on the unit circle.

    <p>0, $\frac{\pi}{2}$, $\frac{3\pi}{2}$, 2</p> Signup and view all the answers

    Is Sin $174^{\circ}$ equal to Sin $6^{\circ}$?

    <p>True</p> Signup and view all the answers

    Find a coterminal angle of $\frac{11\pi}{3}$.

    <p>$\frac{5\pi}{3}$</p> Signup and view all the answers

    Name the trig values corresponding with Csc, Cot, and Sec.

    <p>Sin, Tan, Cos</p> Signup and view all the answers

    What is Csc $60^{\circ}$?

    <p>2/$\sqrt{3}$</p> Signup and view all the answers

    What is Cot $\frac{2\pi}{3}$?

    <p>2</p> Signup and view all the answers

    What is the pattern for the denominators of the unit circle?

    <p>6, 4, 3</p> Signup and view all the answers

    What is $300^{\circ}$ in radians?

    <p>$\frac{5\pi}{3}$</p> Signup and view all the answers

    What is $120^{\circ}$ in radians?

    <p>$\frac{2\pi}{3}$</p> Signup and view all the answers

    What are the difference of degrees from the 3 points on the unit circle?

    <p>30, 45, 60</p> Signup and view all the answers

    What's the difference of the last third point to one of the 4 reference points?

    <p>30</p> Signup and view all the answers

    What is $135^{\circ}$ in radians?

    <p>$\frac{3\pi}{4}$</p> Signup and view all the answers

    What is $150^{\circ}$ in radians?

    <p>$\frac{5\pi}{6}$</p> Signup and view all the answers

    What is $180^{\circ}$ in radians?

    <p>$\pi$</p> Signup and view all the answers

    What is $210^{\circ}$ in radians?

    <p>$\frac{7\pi}{6}$</p> Signup and view all the answers

    What is $225^{\circ}$ in radians?

    <p>$\frac{5\pi}{4}$</p> Signup and view all the answers

    What is $240^{\circ}$ in radians?

    <p>$\frac{4\pi}{3}$</p> Signup and view all the answers

    What is $270^{\circ}$ in radians?

    <p>$\frac{3\pi}{2}$</p> Signup and view all the answers

    What is $300^{\circ}$ in radians?

    <p>$\frac{5\pi}{3}$</p> Signup and view all the answers

    What is $315^{\circ}$ in radians?

    <p>$\frac{7\pi}{4}$</p> Signup and view all the answers

    What is $330^{\circ}$ in radians?

    <p>$\frac{11\pi}{6}$</p> Signup and view all the answers

    What is $360^{\circ}$ in radians?

    <p>$2\pi$</p> Signup and view all the answers

    What does the chart for trigonometry show?

    <p>Angles and their trig values</p> Signup and view all the answers

    Study Notes

    Unit Circle Basics

    • The unit circle has key coordinates for angles, which include points represented as (cos x, sin x) for each angle x.
    • Important values for trigonometric functions are derived from angles associated with the unit circle.

    Common Trigonometric Values

    • Cos(π/3) = 1/2
    • Cos(2π/3) = -1/2
    • Sin(2π/3) = √3/2

    Quadrants and Their Characteristics

    • Quadrant IV contains positive cosine values.
    • Angle 5π/3 is located in Quadrant IV.

    Coterminal Angles

    • Coterminal angles share the same terminal side. Example: 11π/3 is coterminal with 5π/3.

    Reference Points on the Unit Circle

    • Focus points on the unit circle are: 0, π/2, 3π/2, and 2π.
    • Angles on the unit circle are often expressed in radians.

    Trigonometric Identities

    • csc(60°) = 1/sin(60°) => csc(60°) = 2√3/3 after rationalizing.
    • The relationships among sine, cosine, tangent, cotangent, and cosecant are important in solving trigonometric problems.

    Angle Conversion

    • 300° is equivalent to 5π/3 radians.
    • 120° translates to 2π/3 radians.
    • 135° converts to 3π/4 radians.
    • 150° corresponds to 5π/6 radians.
    • Important angles like 210°, 225°, 240°, 270°, 300°, 315°, 330°, and 360° also have specific radian measures.

    Differences and Patterns

    • The differences in angles for points on the unit circle are typically 15°, aligning common unit circle values for calculations.
    • The pattern for the denominators in unit circle values cycles through: 6, 4, 3 in various relationships.

    Summary of Key Points

    • Knowledge of these angles and their trigonometric values is crucial for solving algebraic problems involving the unit circle.
    • True/False examples help confirm understanding of key properties, such as sin(174°) = sin(6°) due to their coterminality.

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    Description

    This quiz covers the fundamental concepts of the unit circle, including key coordinates, common trigonometric values, and the properties of quadrants. You'll also explore coterminal angles and reference points on the unit circle, along with essential trigonometric identities and angle conversions.

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