How do you find sin x and cos x when tan x = 5?

Expert Answers
hala718 eNotes educator| Certified Educator

tanx = 5

We know that `tanx= sinx/cosx`

`` `==gt sinx/cosx = 5 `

`==gt sinx = 5cosx` ..............(1)

Now we will use the identity `sin^2 x + cos^2 x = 1` .......(2)

==> We will substitue (1) into (2).

`==gt (5cosx)^2 + cos^2 x = 1 `

`==gt 25cos^2 x + cos^2 x = 1 `

`==gt 26cos^2 x = 1 `

`==gt cos^2 x = 1/26 `

`==gt cosx = +-sqrt(1/26)` `~~` `+-0.1961` ``

`==gt sinx = 5cosx = +-5*sqrt(1/26)`  `~~ +-0.9806` `` ``

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jacqueshaw | Student

tanx= 5

tanx = sinx/cosx

sin/cosx=5

sinx=5cosx

sin^2 x=(5cosx)^2

sin^2 x=1-cos^2 x

1-cos^2 x=25cos^2 x

25cos^2 x+cos^2 x=1

26cos^2 x=1

cos^2 x=1/26

=+-sqrt(1/26)~~+-0.1961

sinx=5cosx=+-5*sqrt(1/26)~~+-0.9806