Answer:
Step-by-step explanation:
See figure 1 attached
Radius of circle equal 1. This radius is at the same time the hypotenuse of triangle OMP . You can see:
sin∠POM = opposite leg/hypotenuse given that hypotenuse is 1
sin∠POM = opposite leg = PM Note PM never change sign when
rotating from 0 up to π/2 (quadrant one). Its value will be
0 ≤ sin∠POM ≤ 1
cos∠POM = adjacent leg/hypotenuse /hypotenuse given that hypotenuse is 1 then for the same reason
cos∠POM = adjacent leg = OM
OM never change sign in the first quadrant, and can tak vals beteen 1 for 0° up to 1 for π/2
Tan∠POM = sin∠POM /cos∠POM
The last relation is always positive (in the first quadrant) and
tan∠POM = opposite leg/adjacent leg
Answer:
A) sine: positive cosine: positive tangent: positive
Step-by-step explanation:
Consider the first quadrant in the coordinate diagram below:
x and y are positive
[tex]Sin \theta = \dfrac{Opposite}{Hypotenuse} =\dfrac{y}{\sqrt{x^2+y^2} } \\Cos \theta = \dfrac{Adjacent}{Hypotenuse} =\dfrac{x}{\sqrt{x^2+y^2} } \\Tan \theta = \dfrac{Opposite}{Adjacent} =\dfrac{y}{x }[/tex]
For positive x and y, [tex]\sqrt{x^2+y^2}[/tex] is also positive. Therefore:
[tex]Sin \theta[/tex] is positive
[tex]Cos \theta[/tex] is positive
[tex]Tan \theta[/tex] is positive
