If tan(θ)=4/3, 0≤θ≤π2, then explain simple terms please

Question

If , , then

 equals   =

 equals =

   equals   =

Answer 1

We are given tan(θ)=4/3, and we know tan is opposite over adjacent (o/a) so the triangle has two sides given. We need to first determine the last side of the triangle using pythagorean theorem.

Opposite = 4, adjacent = 3

hypotenuse² = opposite² + adjacent²

hypotenuse = √(4² + 3²) = √(25) = 5

Now that we have all of the sides determined, plug them into the questions asked:

sin(θ)  = o / h = 4 / 5

cos(θ) = a / h = 3 / 5

sec(θ) = h / a = 5 / 3

Hope this helped!