Either sin x, cos x or tan x is given. Find the other two if x lies in the specified interval. Sin x = 3/5, x (weird e that looks like pitchfork) [pie, 3pie/2]

Question

I would greatly appreciate any help :)

Answer 1

Hey there Jack,

 

So the piece to start with is the ∈[pi, 3pi/2] which I think is what you meant. 

 

What that tells us is that this triangle is located in quadrant 2 where horizontal values are negative and vertical values are positive

 

Next the equation sin x =3/5 tells us that the opposite (or vertical) side of this triangle is 3 and the hypotenuse is 5

 

There is only one triangle with those side lengths, the 3-4-5 triangle so we know the length of the last side is 4, but we just said we are in quadrant 2 so horizontal values are negative. That means the last side is -4

 

In total

Opposite (vertical) = 3

Adjacent (horizontal) = -4

Hypotenuse = 5

 

Now just remember SOH CAH TOA

 

cos = opp/hyp

 

tan = opp/adj

 

So our final answers are:

 

cos x = -4/5

 

tan x = -3/4

 

Hope that helps!