Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (-2√3,-2) is on the terminal side of θ. then find the exact values of the six trigonometric functions for θ. rationalize denominators when aplicable.

The exact values of the six trigonometric functions are: , , , , , .

An angle in standard position is an angle measured with respect to the +x semiaxis. In this question we must derive the six trigonometric functions from the distances between a given point and the origin. The trigonometric functions are described below:

Sine

(1)

Cosine

(2)

Tangent

(3)

Cotangent

(4)

Secant

(5)

Cosecant

(6)

Where is the terminal angle in sexagesimal degrees.

If we know that and , then the exact values of the six trigonometric functions are:

, , , , ,

, , , , ,

The exact values of the six trigonometric functions are: , , , , , .

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Step-by-step explanation:

We can use the unit circle to figure out the trigonometric functions of θ.

Both the x- and y- coordinates are in the third quadrant, so θ is an obtuse angle (210°), as seen in the figure below.

sinθ = -2/4         = -½

cosθ = (-2√3)/4  = -(√3)/2

tanθ = -2/(-2√3) = 1/√3         = (√3)/3

cscθ = 1/sin θ     = 4/(-2)        = -2

secθ = 1/cosθ     = 4/(-2√3)  = -2/√3 = -(2√3)/3

cotθ = 1/tan θ     = -2√3/(-2) = √3

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: