Please help with finding exact value of sin,tan and sin2(theta)?

I am so confused! Can someone please help me understand how to solve this? Can you please show work so I can better understand also. Please don't just give me the answer because I'm not going to understand. I really need an explanation so that I can see why I'm not understanding.

I re-wrote the answer below and also took a picture of the question if it makes it easier to read.

Thanks so much ahead of time!!! Happy Sunday!

Questions:

Suppose that cos Θ = 4/5 with 3π/2 < θ < 2π.

(a) Find the exact value of sin(Θ). 

(b) Find the exact value of tan(Θ). 

(c) Find the exact value of sin(2Θ ).

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2 Answers

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  • 2 months ago
    Favorite Answer

    This is in Quadrant IV (between 3π/2 and 2π), so sine is negative.

    cos^2 +sin^2 = 1

    (4/5)^2 +sin^2 = 1

    sin^2 = 9/25

    sin = 3/5 ; -3/5

    Choose -3/5

    tan = sin/cos = (-3/5)/(4/5) = -3/4

    sin(2x) = 2sinx*cosx = 2(-3/5)(4/5) = -24/25

  • ted s
    Lv 7
    2 months ago

    somewhat trivial ....the fundamental triangle is { 4 , - 3 , 5 }....so sin Θ = - 3 / 5 , tan Θ = - 3 / 4 , and sin (2Θ) = 2 ( - 3/ 5 ) (4 / 5)

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