Ask questions and get helpful answers.

evaluate the expression under the given conditions.

cos(θ − ϕ); cos(θ) = 5/13, θ in Quadrant IV, tan(ϕ) = − square root15,ϕ in Quadrant II

Anyone know how to do this I have never been this confused in my life

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
1 answer
  1. start with : cos(θ) = 5/13, θ in Quadrant IV
    you should recognize the 5-12-13 right-angled triangle
    and since cosØ = adjacent/hypotenuse
    x = 5, r = 13 , y = -12, since Ø is in IV
    and sinØ = -12/13

    also tan(ϕ) = −√15 = -√15/1 = y/x and ϕ is in II,
    y = √15 , x = -1
    r^2 = x^2 + y^2 = 15+1 = 16
    r = 4
    sinϕ = √15/4 , cosϕ = -1/4

    you must know that:
    cos(θ − ϕ) = cosθcosϕ + sinθsinϕ
    = (5/13)(-1/4) + (-12/13)(√15/4)
    = -5/52 - 12√15/52
    = (-5-12√15)/52

    To do these type of problems you must know your basic trig definitions as well as the CAST rule.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.