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  1. Questions
  2. Trigonometry

1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two

decimal places.

6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin �y

10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ

17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = cos w-cot w cos w

23.Find a counterexample to shows that the equation sec a� – cos a� = sin a� sec a� is not an identity.

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Alonso
1 answer

  1. 1.
    Some students like to look at these types the following way:
    let tanx = y, to get
    y^2 + y - 1 = 0
    by formula ...
    y = (-1 ± √5)/2
    so tanx = (-1 ± √5)/2
    using your calculator ....
    x = 31.72° or 211.72°

    or tanx = (-1 - √5)/2
    x = 121.72° or 301.72°

    #6, 10, 17,
    establish correct order of operation, by using brackets.

    #23
    just pick any angle you want and use your calculator
    or pick a = 30°, (you should know the trig values for 30°)

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    Reiny

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