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:
sinā POM Ā = opposite leg/hypotenuse Ā given that hypotenuse is 1
sinā POM = Ā opposite leg = PM Ā Note PM never change sign when
rotating from 0 up to Ļ/2 Ā (quadrant one). Ā Its value will be
0 ā¤ sinā POM ā¤ 1
cosā POM = adjacent leg/hypotenuse /hypotenuse Ā given that hypotenuse is 1 Ā then for the same reason
cosā POM = adjacent leg = OM
OM never change sign in the first quadrant, and can tak vals beteen 1 for 0Ā° up to 1 for Ļ/2
Tanā POM = sinā POM /cosā POM
The last relation is always positive (in the first quadrant) and
tanā 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
