For the acute angle with sin theta=3/5, find cos theta, tan, cot, csc, sec.

Answer 1

Draw the triangle. Isn't it a 3,4,5 triangle?

Answer 2

For an acute angle θ, and sin(θ)=3/5, all the other five functions will be positive.

Draw a right-triangle and label one of the acute angles θ.

Label the length of the hypothenuse as 5, the side opposite θ as 3. Confirm that sin(θ) is 3/5.

Calculate the adjacent (remaining) side length by Pythagoras's theorem, namely L=√(5²-3²)=4. Label the length of the adjacent side 4.

Now from the fundamental definitions of the functions, determine the trigonometric ratios of each from:

sin(θ) = opposite/hypothenuse
cos(θ) = adjacent/hypothenuse
tan(θ) = opposite/adjacent
csc(θ) = hypothenuse/opposite
sec(θ) = hypothenuse/adjacent
cot(θ) = adjacent/opposite