For the acute angle θ with sinθ=3/5, find (give exact answers, NO DECIMALS)

Question

cosθ=

tanθ=

cotθ=

secθ=

cscθ=

Answer 1

If θ is acute, and sin(θ) is 3/5, a right triangle with the opposite side of 3 units and hypotenuse of 5 will have an adjacent side of 4 (by Pythagoras's theorem).

Hence cos(θ) = 4/5,

tan(θ) = 3/4

cot(θ) = 1/tan(θ) =4/3

sec(θ) = 1/cos(θ) = 5/4

and csc(θ) = 1/sin(θ) = 5/3