Question

Given the triangle below, find the correct value of the six trigonometric functions

Answer 1

Chek below, please.

1) Examining that triangle, we can state that this is a Pythagorean Triple therefore, that hypotenuse is 5

`\begin{gathered} a^2=3^2+4^2 \\ a^2=9+16 \\ a^2=25 \\ a=5 \end{gathered}`

2) So now, we can write out the following trig ratios, considering the acronyms for these trig ratios:

0. sin(θ) = Opposite/hypotenuse

,

1. cos(θ) = adjacent/hypotenuse

,

2. tan(θ)=opposite/adjacent

,

3. csc(θ)=1/sin(θ)

,

4. sec(θ)=1/cos(θ)

,

5. cot(θ)=1/tan(θ)

3) So, the answer is: