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Find the values of the trigonometric functions of t from the given information.

tan(t) = −5,  csc(t) > 0

sin(t) = 

 

 cos(t) = 

 

 csc(t) = 

 

 sec(t) = 

 

 cot(t) = 

Guest Apr 25, 2018
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Since the tangent is negatie and the csc is positive....  " t "  must fall into the second quadrant

 

tan t  =  -5 / 1    =   5 / - 1 =   y / x

 

We need to find r   =  √  [ x^2 + y^2]  =  √ [ (-1)^2  + 5^2 ]  = √26

 

sin t  =  y / r  =  5 / √26  =   (5/26)√26

cos t  =  x / r  =  -1 / √26  =  -√26/26

csc t  =   r / y  =  √26 / 5

sec t   =  r / x =  √26 / - 1    =  -√26

cot t  =  x / y  =   -1/5

 

And there you go  !!!

 

 

cool cool cool

CPhill  Apr 25, 2018

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