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

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 2

A) sine: positive cosine: positive tangent: positive

Explanation:

Consider the first quadrant in the coordinate diagram below:

x and y are positive

`Sin \theta = (Opposite)/(Hypotenuse) =(y)/(√(x^2+y^2) ) \\Cos \theta = (Adjacent)/(Hypotenuse) =(x)/(√(x^2+y^2) ) \\Tan \theta = (Opposite)/(Adjacent) =(y)/(x )`

For positive x and y,
`√(x^2+y^2)` is also positive. Therefore:

`Sin \theta` is positive

`Cos \theta` is positive

`Tan \theta` is positive