ok the csc (cosecant) thing is really messing me up. Help?

Question

ok the question asks :
Suppose that 0 < t < pi/2, and csc t = 4. Find the values of the trigonometric functions sin(t), cos(t) and tan(t).

how am i supposed to do that with just cosecant?

Answer 1

1 / sin t = 4
sin t = 1 / 4
t = 14.5°
cos 14.5° = 0.968
tan 14.5° = 0.259

Answer 2

Draw a right triangle. Then call one angle t. csc=hyp/opp.So Set opp=1 and hyp=4. Then find sin, cos and tan(t) but make sure t is in between 0 and pi. This goes in the homework help section under the Education and Reference section.

Answer 3

By using the definition of cosecant, definitions of sin, cos, tan and Pythagorean theorem.

csc(t) can be written as
csc(t) = 1/sin(t)

So,
csc(t) = 4
4 = 1/(sin(t)
sin(t) = 1/4

now sin(t) is just the ratio of 2 sides of a triangle... the opposite and the hypotenuse
opp = 1
hyp = 4

by Pythagorean theorem
adj = sqrt(4^2-1^2)
adj = sqrt(15)
you know this is positive because the adjacent side is positive in the first quadrant (0,p/2)


so you know
opp = 1
adj = sqrt(15)
hyp = 4


You can figure out any trig function just by using the definition
cos(t) = adj/hyp
cos(t) = sqrt(15)/4

tan(t) = sin(t)/cos(t) or tan(t) = opp/adj

tan(t) = 1/ [sqrt(15)]
tan(t) = sqrt(15)/15