Find the exact value of each of the remaining trigometric functions of theta

Question

sin theta equals -5/13, tan theta is greater than 0

Answer 1

 

Hi Zach,

 

Recall that sinθ is negative and tanθ is positive

 

in the third quadrant of x-y axis,

 

in which cosθ is negative. 

 

According to the rule sin²θ + cos²θ = 1

 

or the Pythagorean theorem,

 

we can get cosθ = -12/13.

 

Then, from tanθ = sinθ/cosθ,

 

we get tanθ = 5/12.

 

 

 

Answer 2

Sinθ = -5/13, cos θ= -12/13, tanθ= 5/12, cscθ= -13/5, secθ=-13/12, cotθ=12/5