SOLUTION: Suppose sin t = 4/7 and cos t < 0. Find each of the following (exact values): cos t = tan t = csc t = sec t = cot t = Please explain Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose sin t = 4/7 and cos t < 0. Find each of the following (exact values): cos t = tan t = csc t = sec t = cot t = Please explain Thank you      Log On


   

Question 986632: Suppose sin t =
4/7
and cos t < 0. Find each of the following (exact values):

cos t =
tan t =
csc t =
sec t =
cot t =
Please explain
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
cos%5E2%28t%29%2Bsin%5E2%28t%29=1
cos%5E2%28t%29=1-%284%2F7%29%5E2
highlight%28cos%28t%29=sqrt%281-%284%2F7%29%5E2%29%29

Use the definitions for the other functions.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose sin t =
4/7
and cos t < 0. Find each of the following (exact values):

cos t =
tan t =
csc t =
sec t =
cot t =
Please explain
Thank you
I'll do the first

Since sin (t) > 0, and cos (t) < 0, angle t is in the 2nd quadrant

sin+%28t%29+=+O%2FH+=+4%2F7

A%5E2+=+H%5E2+-+O%5E2

A%5E2+=+7%5E2+-+4%5E2

A+=+sqrt%287%5E2+-+4%5E2%29

A+=+sqrt%2849+-+16%29

A+=+sqrt%2833%29, but since cos < 0, A+=+-+sqrt%28+33%29

highlight_green%28cos+%28t%29+=+%28-+A%29%2FH+=+%28-+sqrt%2833%29%29%2F7%29  

You now know A, O, and H, and so you should be able to find the other 4 trig. functions, remembering that: csc will be positive, while sec, tan, and cotan will be negaive