SOLUTION: Find the values of the trigonometric functions of t from the given information. tan t = −8, csc t > 0 sin t = cos t= tan t= sec t= csc t= cot t=

Algebra ->  Trigonometry-basics -> SOLUTION: Find the values of the trigonometric functions of t from the given information. tan t = −8, csc t > 0 sin t = cos t= tan t= sec t= csc t= cot t=      Log On


   

Question 841711: Find the values of the trigonometric functions of t from the given information.
tan t = −8, csc t > 0
sin t =
cos t=
tan t=
sec t=
csc t=
cot t=
Found 2 solutions by fcabanski, lwsshak3:
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
The angle must be located in the 2nd quadrant. In the second quadrant: sin and csc are positive, while cos, sec, tan, and cot are negative.


tan(t) = 8. tan = opp/adj. Pick any numbers for opp/adj such that the quotient is 8. Don't worry about the sign of your answers. The quadrant (2nd) tells you the sign of each of the functions.


tan(t)= 8 = 8/1. Opposite side is 8, adjacent side is 1. The hypotenuse is sqrt%288%5E2+%2B+1%5E2%29+=+sqrt%2865%29


Now you can find all of the requested values. Remember, only sin and csc are positive:


sin(t) = opp/hyp = 8%2Fsqrt%2865%29 = approximately .992


csc(t) = 1/(sin(t) = 1/.992 = approximately 1.008


cos(t) = adj/hyp = 1%2Fsqrt%2865%29 = appox. -.124. Remember, cos is negative in the second quadrant. Don't worry about the sign, until you complete the calculation. Then add the sign based on the quadrant.
sec(t) = 1/cos(t) = 1/(-.124) = appox. -8.062.


tan(t) is already given: -8. cot(t) is 1/tan(t) = -1/8


Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the values of the trigonometric functions of t from the given information.
Given data shows reference angle t is in quadrant II where sin>0, cos<0, tan<0.
Hypotenuse of reference right triangle=√(8^2+1^2)=√(64+1)=√65
tan t= −8, csc t > 0
sin t=8/√65=8√65/65
cos t=-1/√65=-√65/65
tan t=-8
sec t=-√65
csc t=√65/8
cot t=-1/8