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Cofunctions of Complementary Angles quiz

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  • What is the definition of complementary angles?
    Complementary angles are two angles whose measures add up to 90 degrees.
  • In a right triangle, why are the two non-right angles always complementary?
    Because the right angle is 90 degrees and the sum of all angles in a triangle is 180 degrees, the other two angles must add up to 90 degrees.
  • What does the complementary angle theorem state about cofunctions?
    The complementary angle theorem states that cofunctions of complementary angles are equal.
  • What is a cofunction identity in trigonometry?
    A cofunction identity describes how two trigonometric functions are related through their complementary angles.
  • What is the cofunction identity for sine and cosine?
    The sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ).
  • If sin(53°) = cos(37°), what is the relationship between 53° and 37°?
    53° and 37° are complementary angles because they add up to 90°.
  • How do you find the cofunction of tan(16°)?
    The cofunction of tan(16°) is cot(74°), since 74° is the complement of 16°.
  • What is the cofunction of sec(0°)?
    The cofunction of sec(0°) is csc(90°).
  • How do you express cos(5π/18) in terms of its cofunction using radians?
    cos(5π/18) = sin(π/2 - 5π/18), which simplifies to sin(2π/9).
  • What is the general formula for finding the cofunction of an angle θ in degrees?
    The cofunction of an angle θ is the corresponding cofunction evaluated at (90° - θ).
  • How do you use cofunction identities to solve an equation like sin(x - 10) = cos(x)?
    Rewrite cos(x) as sin(90° - x), then set the arguments equal: x - 10 = 90 - x, and solve for x.
  • What is the solution for x in the equation sin(x - 10) = cos(x)?
    x = 50.
  • When solving cos(θ) = sin(2θ - 30), what is the first step using cofunction identities?
    Rewrite cos(θ) as sin(90° - θ) so both sides have the same trigonometric function.
  • After rewriting cos(θ) = sin(2θ - 30) as sin(90° - θ) = sin(2θ - 30), what do you do next?
    Set the arguments equal: 90 - θ = 2θ - 30, and solve for θ.
  • What is the value of θ that solves cos(θ) = sin(2θ - 30)?
    θ = 40 degrees.