Pre-Calculus 12 Section 6.1: Trigonometric Basics
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Questions and Answers

What determines the vertex of an angle?

  • The endpoint of the rotating arm (correct)
  • The coordinate plane
  • The rotating arm
  • The direction of rotation

    • What is the direction of rotation that forms a positive angle 𝜃?

  • Clockwise direction
  • Counter-clockwise direction (correct)
  • Horizontal direction
  • Diagonal direction

    • What is an angle called if its vertex is at the origin and it originates from the positive 𝒙 − 𝒂𝒙𝒊𝒔?

  • Obtuse angle
  • Standard angle
  • Standard Position angle (correct)
  • Right angle

    • What type of angle is formed when the terminal arm is rotated clockwise about the vertex?

    <p>Negative angle</p> Signup and view all the answers

    What is the term for the arm that rotates around the vertex?

    <p>Terminal arm</p> Signup and view all the answers

    What is the range of a reference angle?

    <p>0° ≤ 𝜃′ ≤ 90°</p> Signup and view all the answers

    What is the formula to find the reference angle for 𝜃 in Quadrant 2?

    <p>𝜃′ = 180° − 𝜃</p> Signup and view all the answers

    What is the reference angle for a rotation of 200°?

    <p>20°</p> Signup and view all the answers

    What is the definition of a radian?

    <p>An angle of 1 radian, rotated counter-clockwise, of arc length of 1 on a unit circle</p> Signup and view all the answers

    What is the unit circle used for?

    <p>To measure the arc length of a circle</p> Signup and view all the answers

    What is the circumference of a unit circle?

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

    What is the purpose of radians in science and engineering?

    <p>To measure the arc length of a circle</p> Signup and view all the answers

    What is the relationship between degrees and radians in one full rotation?

    <p>360° = 2π</p> Signup and view all the answers

    What is the radian measure of 45°?

    <p>π/4</p> Signup and view all the answers

    What is the degree measure of 5π/6 radians?

    <p>225°</p> Signup and view all the answers

    What is the simplified form of the radian measure of 315°?

    <p>7π/4</p> Signup and view all the answers

    What is the degree measure of 2.5 radians?

    <p>143°</p> Signup and view all the answers

    What is the term for angles in Standard Position that have the same terminal side?

    <p>Co-Terminal Angles</p> Signup and view all the answers

    What is the result of adding 360° to a given angle?

    <p>A co-terminal angle</p> Signup and view all the answers

    How do you find the smallest positive co-terminal angle for a given angle?

    <p>Divide the given angle by 360 to find the number of full rotations</p> Signup and view all the answers

    What is the reference angle for a given angle 𝜽 in Standard Position?

    <p>The positive acute angle formed with the terminal side of 𝜽 and the 𝒙-axis</p> Signup and view all the answers

    If 𝜃 = 120°, what is one of the negative angles that are co-terminal with 𝜃?

    <p>−240°</p> Signup and view all the answers

    What is the result of subtracting 2(360°) from a given angle?

    <p>A co-terminal angle</p> Signup and view all the answers

    What is the radian measure of the angle 𝒔, given that 𝒔 = 4.8 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 and 𝒔 = 24𝑐𝑚?

    <p>5.33 𝑟𝑎𝑑𝑖𝑎𝑛𝑠</p> Signup and view all the answers

    In which quadrant is the angle 1100°?

    <p>Not in a specific quadrant</p> Signup and view all the answers

    What is the degree measure of the rotation 1/6 of a full rotation?

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

    What is the radian measure of the angle 90° in terms of 𝜋?

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

    What is the coterminal angle of 150° in the range [-360°, 0°)?

    <p>-450°</p> Signup and view all the answers

    What is the radian measure of the angle 630°, expressed to three decimals?

    <p>10.995 𝑟𝑎𝑑𝑖𝑎𝑛𝑠</p> Signup and view all the answers

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