Question

Determine the value of the signs of the functional values of sine, cosine and tangent in quadrant one. a. sine: positive cosine: positive tangent: positive c. sine: positive cosine: positive tangent: negative b. sine: negative cosine: negative tangent: negative d. sine: negative cosine: positive tangent: negative

Answer 1

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

$Sin \theta = \dfrac{Opposite}{Hypotenuse} =\dfrac{y}{\sqrt{x^2+y^2} } \\Cos \theta = \dfrac{Adjacent}{Hypotenuse} =\dfrac{x}{\sqrt{x^2+y^2} } \\Tan \theta = \dfrac{Opposite}{Adjacent} =\dfrac{y}{x }$

For positive x and y, $\sqrt{x^2+y^2}$ is also positive. Therefore:

$Sin \theta$ is positive

$Cos \theta$ is positive

$Tan \theta$ is positive

Answer 2

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