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Math Help - angles

  1. #1
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    angles

    Dad gave me about 50 problems to sharpen my skills for the up coming school year...

    Im having a few problems....Please help

    1. Find the period of the graph of the equation y=2sin(pi x-3)


    2. Find all solutions to the equation cos x=-1


    choices

    a. x= pi n
    b. x= 2pi n
    c. x= pi/2+ pi n
    d. x= pi + 2 pi n


    3. Use the addition and subtraction formula to simplify cos(x+pi)


    Ya'll are great thanks
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  2. #2
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    Hello, ccdalamp!

    3. Use the addition and subtraction formula to simplify \cos(x+\pi)
    We're expected to know: . \cos(A \pm B) \;=\;\cos(A)\cos(B) \mp \sin(A)\sin(B)


    We have: . \cos(x + \pi) \;=\;\cos(x)\cos(\pi) - \sin(x)\sin(\pi)


    We're also expected to know that: . \cos(\pi) = -1 .and . \sin(\pi) = 0

    Therefore, we have: . \cos(x)\!\cdot\!(-1) - \sin(x)\!\cdot\!(0) \;=\;-\cos(x)

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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ccdalamp View Post
    Dad gave me about 50 problems to sharpen my skills for the up coming school year...

    Im having a few problems....Please help

    1. Find the period of the graph of the equation y=2sin(pi x-3)
    see my first post here

    2. Find all solutions to the equation cos x=-1


    choices

    a. x= pi n
    b. x= 2pi n
    c. x= pi/2+ pi n
    d. x= pi + 2 pi n
    the cosine function hits -1 once in every period. so if we can find one instance where it hits -1, in say, 0 \leq x \leq 2 \pi for x in radians, we can just supplement that by adding some constant times 2 \pi to get the value for any other period, since all the -1
    s will be a period apart (which is 2 \pi for cos(x))

    cos(x) = -1 when x = pi in the period [0,2pi]

    thus all solutions can be given by: x = \pi + 2n \pi for n an integer. which is choice d
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