Question

If sin Θ = 2/7 and tan Θ > 0, what is the value of cos Θ?

Answer 1

3 square root of 5 over 7
negative 3 square root of 5 over 7
3 square root of 5
negative 3 square root of 5

Answer 2

cos and tan are negative, so we are in the second quadrant. The angle must lie between pi/2 and pi.

cos = adjacent side / hypotenuse = -2/7
adjacent side = 2
hypotenuse = 7

opposite side = sqrt(7^2-2^2) = sqrt(49-4)=sqrt(45) = 3sqrt(5)

sin (theta) = opposite side / hypotenuse = 3sqrt(5)/7
sin is positive in the second quadrant

tan(theta) = sin(theta)/cos(theta) = (-2/7) / (3sqrt(5)/7)
= -2/3sqrt(5)

cot(theta) = 1/tan(theta) = -3sqrt(5)/2

sec(theta) = 1/cos(theta) = -7/2

csc(theta)=1/sin(theta) = 7/3sqrt(5)

Answer 3

With that, you're saying that cos is -2/7 but in my problem it says that sin is 2/7. I'm confused on how you got that. @Agl202

Answer 4

Ya, ur right! Sorry, for my mistake...

Answer 5

It's okay, I was just a bit confused on how you got solved for sin, when sin was already given haha.

Answer 6

Lol, sorry again.

Answer 7

I think I get it though. Thanks for giving an example. I remember going over this in class, but I completely forgot how to do it.

Answer 8

allrighty! :)