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Math Help - Trigonometric Quotient Identities

  1. #1
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    Trigonometric Quotient Identities

    I wouldn't normally ask, but I'm trying to make a chart of trigonometric identities (beyond the most fundamental) so that I don't have to calculate the same things over and over.

    So, tan x * cos x = sin x

    But, what is tan/cos? I thought it was sin/cos^2, but I'm not sure.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Picatta View Post
    I wouldn't normally ask, but I'm trying to make a chart of trigonometric identities (beyond the most fundamental) so that I don't have to calculate the same things over and over.

    So, tan x * cos x = sin x

    But, what is tan/cos? I thought it was sin/cos^2, but I'm not sure.
    tan x = \frac{sin x}{cos x}

    tan x \times cos x = sin x

    Now we want to get rid of that cos x and we also want cos x in the denominator. Divinding by cos^2 x should fix that. Recall that we have to do the same thing to both sides of the equation.

    \frac{tan x}{cos x} = \frac{sin x}{cos^2 x}

    So you were correct!

    ============================

    EDIT: An even easier way...

    tan x = \frac{sin x}{cos x}

    Divide by cos  x both sides.

    \frac{tan x}{cos x} = \frac{sin x}{cos^2 x}
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