Question

Hey, I'm struggling on this question:

tan x = 2/3 and 0 < X < Pie/2
Find the exact values for sin x and cos x

It's Trigonometry Unit of a Circle :) If you could answer it I'll appreciate it greatly!

Answer 1

Hi @popkov98
first, do you know the unit circle?

Answer 2

Yea it's quadrant 1
so sin cos and tan all positive

Answer 3

Couldn't get the pie symbol on my computer

Answer 4

sweet, so tan^-1 of 2/3 = 0.588003 radians
and 2 pi radians = 1 full circle
so we're looking for something between 0 radians ( 0 degrees) and pi/2 radians (90 degrees)

Answer 5

so this is the best image i can think of for explaining it

Answer 6

We have use trig identities though, like cos^2x + sin^2x = 1 ... tan x = sin x / cos x

Answer 7

Does anyone know? Please help!

Answer 8

so if you remember SOH CAH TOA
in our example, tan x = 2/3
we know we're aiming for the first quadrant, where all are positive
so tan x = opposite/ adjacent = 2/3

tan x = (sine x )/ (cos x)
so 2/3 = sin x /cos x
sin x = (2/3) * (cos x)

cos x = (3/2) * (sin x)

Answer 9

Hmmm, that doesn't really help because we should get an answer somewhat like this;

Answer 10

so if you work out the triangle, h^2 = a^2 + b^2
a = 3, b = 2
so h = sqrt 13

so from SOH CAH TOA
CAH cos x = adjacent / hypotenuse
cos x = 3/sqrt 13

Answer 11

and sin x (SOH)
sin x = opposite / hypotenuse
sin x = 2 / sqrt 13

Answer 12

Oh wow, thanks so much! That's exactly the right answers!

Answer 13

cool man, all good hey

Answer 14

If it's not a bother could you show me how to do it using the formula in the picture I uploaded, if you know that method of solving :)?