if tan0=5/8 and 0 is in the third quadrant, what are the five other remaining trig functions of 0

Question

i need help with this, someone help me

Answer 1

Hi Chris,

 

OK so what do you know 

 

We have a triangle in the third quadrant with a tan = 5/8

 

tan = opp/adj  and in the coordinate plane it equals y/x, you also know that x and y are negative in the third quadrant

 

we can also find the hypothenuse(hyp) since we have the two legs

 

5² + 8² = hyp²

 

25 + 64 = hyp²

 

hyp = sqrt(89)

 

opp = y = -5

adj = x = -8

hpy = sqrt(89)

 

sin = opp/hyp

sin = -5/sqrt(89) 

     = -5*sqrt(89)/89    (multiply numerator and denominator by sqrt(89) to clear it from the denominator

 

cos = adj/hyp

 

tan = 5/8

 

csc = hyp/opp

 

sec = hyp/adj

 

cot = adj/opp

 

With all the information given you should now be able to find these values

 

Hope this helps