1. The point (-11/61,-60/61) on the unit circle U corresponds to an angle of t.
ID: 3026550 • Letter: 1
Question
1. The point (-11/61,-60/61) on the unit circle U corresponds to an angle of t. Find the exact values of the trigonometric functions at t. Enter your answers as fractions, e.g. 1/2
sin t = cos t = tan t =
csc t = sec t = cot t =
2. Use fundamental identities to find the values of the trigonometric functions (as decimal values within .001) for the given conditions.
sin(t) = -0.99
sec(t) > 0
sin t = cos t = tan t =
csc t = sec t = cot t =
3. Use fundamental identities to find the values of the trigonometric functions (as decimal values within .001) for the given conditions.
sin(t) = -0.48
cot(t) < 0
sin t = cos t = tan t =
csc t = sec t = cot t =
Explanation / Answer
sin t = perpendicular / hypotenuse
= -60/61 / 1 = -60/61
cos t = base / hypotenuse
= -11/61
tan t = perpendicular / base
= 60/11
csc t = 1 / sin t = - 61/ 60
sec t = 1/ cos t = -61 / 11
cot t = 1 / tan t = 11/60
2) sin t = -0.99
sin = perpendicular / hypotenuse
base = sqrt ( 1^2 - .99^2 ) = 0.14106
cos t = base / hypotenuse = 0.14106
tan t = perpendicular /base = -0.99 / 0.14106 = -7.018
csc t = -1/0.99 = -1.010
sec t = 1/.14106 = 7.089
cot t = 1/-7.018 = 0.142
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