If sin t = 3/5 and terminal point t is in quadrant II (are my answers correct + a little help)

Question

Find

 

sin t =

cos t =

tan t =

 

csc t =

sec t =

cot t =

 

this is what I have so far

 

sin t = 3/5

cos t = 4/5

tan t = ?

 

csc t = 5/3

sec t = 5/4

cot t = ?

 

Wanted to know if my answers are correct and how would I find the tan t 

Answer 1

You are given sin t. We can use the identity    sin² t + cos² t = 1    to find cos t.

 

 

cos t = √(1 - sin² t)

 

cos t = √(1 - (3/5)(3/5))

 

cos t = √(1 - (9/25))

 

cos t = √((25 - 9) / 25))

 

cos t = √(16 / 25)

 

cos t = 4 / 5

 

Since cosine is negative in the quadrant 2, cos t will be -4/5.

 

 

Then you are going to use these identities to find the other values:

 

tan t = sin t / cos t

 

cot t = cos t / sin t

 

sec t = 1 / cos t

 

csc t = 1 / sin t

Answer 2

tan t = sin/cos=3/4

csc t =1/sin=5/3

sec t=1/cos=5/4

cot t =1/tan=4/3