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
<pre>I'll do the first
Since sin (t) > 0, and cos (t) < 0, angle t is in the 2<sup>nd</sup> quadrant
{{{sin (t) = O/H = 4/7}}}
{{{A^2 = H^2 - O^2}}}
{{{A^2 = 7^2 - 4^2}}}
{{{A = sqrt(7^2 - 4^2)}}}
{{{A = sqrt(49 - 16)}}}
{{{A = sqrt(33)}}}, but since cos < 0, {{{A = - sqrt( 33)}}}
{{{highlight_green(cos (t) = (- A)/H = (- sqrt(33))/7)}}}  
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