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Math Help - Solving Trigonometric Equations

  1. #1
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    Solving Trigonometric Equations

    I am having some serious problems with this section. My book is no use to me. Thanks for all the help! It says: use the basic identities to change the expression to one involving only sines and cosines. Then simplify to a basic trigometric function.

    1). (sinx)(tanx+cotx)

    2). sinx-tan(x)cos(x)+ cos(pi/2-x)

    3). sin(x)cos(x)tan(x)sec(x)csc(x)
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  2. #2
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    Quote Originally Posted by bcavanaugh34 View Post
    I am having some serious problems with this section. My book is no use to me. Thanks for all the help! It says: use the basic identities to change the expression to one involving only sines and cosines. Then simplify to a basic trigometric function.

    1). (sinx)(tanx+cotx)

    2). sinx-tan(x)cos(x)+ cos(pi/2-x)

    3). sin(x)cos(x)tan(x)sec(x)csc(x)
    The basic identities for 1. are...

    tanx=\frac{sinx}{cosx}

    cotx=\frac{cosx}{sinx}

    You now need to simplify

    sinx\left(\frac{sinx}{cosx}+\frac{cosx}{sinx}\righ  t)

    For 3. you need two more

    secx=\frac{1}{cosx}

    cscx=\frac{1}{sinx}

    I recommend you try those first as you should find 2. more challenging
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  3. #3
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    Quote Originally Posted by bcavanaugh34 View Post
    I am having some serious problems with this section. My book is no use to me. Thanks for all the help! It says: use the basic identities to change the expression to one involving only sines and cosines. Then simplify to a basic trigometric function.

    1). (sinx)(tanx+cotx)

    2). sinx-tan(x)cos(x)+ cos(pi/2-x)

    3). sin(x)cos(x)tan(x)sec(x)csc(x)
    Hi bcavanaugh34,

    [1] \sin x(\tan x + \cos x)


    =\sin x \left(\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}\right)


    =\sin x \left(\frac{\sin^2 x+\cos^2 x}{\sin x \cos x}\right)

    {\color{red}\sin^2 x+\cos^2 x = 1}


    =\frac{1}{\cos x}


    [2] \sin x - \tan x \cos x + \cos \left(\frac{\pi}{2}-x\right)


    {\color{red}\cos \left(\frac{\pi}{2}-x\right)=\sin x} <===== Co-Function Identity


    =\sin x - \frac{\sin x}{\cos x}\cos x + \sin x


    =\sin x - \sin x + \sin x


    =\sin x


    You can try [3] now.

    Sorry, Archie, I'm working too slow. But, anyway.....
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