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What is tan x if cos x =-3/5?

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greenbel | Honors

Posted July 24, 2013 at 4:44 AM via web

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What is tan x if cos x =-3/5?

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mjripalda | High School Teacher | (Level 3) Educator

Posted July 24, 2013 at 6:03 AM (Answer #1)

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`cos x=-3/5`

To solve for tan x, apply the formula:

`tan x= sinx/cosx`

But the value of sin x is not given. So, apply the Pythagorean identity to get its value.

`sin^2x+cos^2x=1`

Plug-in cos x=-3/5.

`sin^2x+(-3/5)^2=1`

`sin^2x+9/25=1`

`sin^2x=1-9/25`

`sin^2x=16/25`

`sinx=+-sqrt(16/25)`

`sinx=+-4/5`

Now that the value of sine is known, plug-in `cos x=-3/5` and `sinx=+-4/5` to the formula of tangent.

`tan x= sinx/cosx=(4/5)/(-3/5)=(4/5)*(-5/3)=-4/3`

`tanx = sinx/cosx=(-4/5)/(-3/5)=(-4/5)*(-5/3)=4/3`

Hence,   `tan x=+-4/3` .

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