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Math Help - Need help! (Precalculus)

  1. #1
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    Need help! (Precalculus)

    I have 7 problems that I need help with. If you know just one, it would be EXTREMELY helpful!

    1. Find all solutions to csc x= -1.15 in the interval 0<x<2pi.

    2. Solve 15cos^2(x) - 7cosx-4=0 by factoring and find solutions in 0<x<2pi.

    3. Use appropriate addition formula to simplify cos(A-B) given sec(A) = -2/√3 where 90<A<180 and tan(B) = 1/4 where 0<B<90

    4. Find all solutions of 2sin^2(x) - 9sin(x)+4=0. Express in radians

    5. Find all solutions to sin(3x) = -√2/(2) in interval 0<x<2pi.

    6. Find all solutions for 2sin(x) = √2cos(2x) in interval 0<x<2pi.

    7. Verify the following identity: cos(4x) = 8cos^4(x) - 8cos^2(x) + 1.

    Thank you!
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, madetorder!

    Here's some help . . .


    2. Solve 15\cos^2\!x - 7\cos x-4\:=\:0 by factoring and find solutions in 0\,<\,x\,<\,2\pi
    They told you what to do ... where is your difficulty?


    Factor: . (5\cos x - 4)(3\cos x + 1) \:=\:0

    . . 5\cos x-4\;=\:0\quad\Rightarrow\quad\cos x\:=\:\frac{4}{5}\quad\Rightarrow\quad x\:\approx\:0.6435,\;5.6397

    . . 3\cos x+1\:=\:0\quad\Rightarrow\quad\cos x\:=\:-\frac{1}{3}\quad\Rightarrow\quad x\:\approx\:1.9106,\;4.3726



    7. Verify the following identity: . \cos4x \:= \:8\cos^4\!x - 8\cos^2\!x + 1.
    Recall that: . \cos2\theta \:=\:2\cos^2\!\theta-1


    We have: . \cos4x \;=\;2\cos^2\!2x - 1

    . . . . . . . . . . . . = \;2(2\cos^2\!x - 1)^2 - 1

    . . . . . . . . . . . . = \;2(4\cos^4\!x - 4\cos^2\!x + 1) - 1

    . . . . . . . . . . . . = \;8\cos^4\!x - 8\cos^2\!x + 2 - 1

    . . . . . . . . . . . . = \;8\cos^4\!x - 8\cos^2\!x + 1

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