if tan(t)=3/4 and 0<t<Pi/2 what are sin(t), cos(t), sec(t), cot(t)

Question

Having trouble figuring this one out..

Answer 1

Since 0<t<π/2, then sin(t)>0, cos(t)>0, sec(t)=1/cos(t)>0, and cot(t)=1/tan(t)>0. Always helps to draw right triangles with labelled sides for these kinds of problems.

tan(t) = Opposite/Adjacent = 3/4

sin(t) = Opposite/Hypotenuse = 3/√(3²+4²) = 3/5

cos(t) = Adjacent/Hypotenuse = 4/5

sec(t) = Hypotenuse/Adjacent = 5/4

cot(t) = Adjacent/Opposite = 4/3

Therefore, sin(t)=3/5, cos(t)=4/5, sec(t)=5/4, and cot(t)=4/3 given 0<t<π/2.

Hope this helped!