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Reference Angles quiz

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  • What is a reference angle?
    A reference angle is the acute angle formed between the terminal side of a given angle and the nearest x-axis, always measured as a positive value.
  • How do you find the reference angle for an angle in quadrant 2?
    Subtract the angle from 180 degrees (or π radians) to get the reference angle.
  • Which trigonometric function is always positive in quadrant 2?
    Sine is always positive in quadrant 2.
  • How do you find the reference angle for an angle in quadrant 3?
    Subtract 180 degrees (or π radians) from the angle to get the reference angle.
  • Which trigonometric function is always positive in quadrant 3?
    Tangent is always positive in quadrant 3.
  • How do you find the reference angle for an angle in quadrant 4?
    Subtract the angle from 360 degrees (or 2π radians) to get the reference angle.
  • Which trigonometric function is always positive in quadrant 4?
    Cosine is always positive in quadrant 4.
  • What is the mnemonic to remember which trig function is positive in each quadrant?
    The mnemonic is ASTC: All Students Take Calculus.
  • What are coterminal angles?
    Coterminal angles are angles that share the same terminal side, found by adding or subtracting multiples of 360° or 2π radians.
  • How do you find the coterminal angle of 390 degrees?
    Subtract 360 degrees to get 30 degrees, so 390° and 30° are coterminal.
  • What is the reference angle for 225 degrees?
    The reference angle for 225 degrees is 45 degrees.
  • How do the trig values of an angle relate to its reference angle?
    The trig values are the same as those of the reference angle, but may differ in sign depending on the quadrant.
  • What is the cosine of negative π/4?
    The cosine of negative π/4 is √2/2, the same as the cosine of its coterminal angle 7π/4.
  • How do you determine the sign of a trig function in a given quadrant?
    Check which axis values (x or y) are positive or negative in that quadrant, or use the ASTC mnemonic.
  • What is the sine of 390 degrees?
    The sine of 390 degrees is 1/2, the same as the sine of 30 degrees.