Question

Sketch an angle theta in standard position such that theta has the least possible positive measure and the point (-2, Square root three) is on the terminal side of theta. Then find the exact values of the six trigonometric functions for each angle

Answer 1

A sketch of the angle is attached and the  six trigonometric functions for each angle are;

sinθ = -½

cosθ = -(√3)/2

tanθ = (√3)/3

cscθ = -2

secθ = -(2√3)/3

cotθ = √3

How to find the trigonometric ratios?

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.

An angle in standard position is an angle measured with respect to the +x semi-axis. 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:

sinθ = -2/4 = -½

cosθ = (-2√3)/4  = -(√3)/2

tanθ = -2/(-2√3) = 1/√3  = (√3)/3

cscθ = 1/sin θ  = 1/-½  = -2

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

cotθ = 1/tan θ = -2√3/(-2) = √3

Read more about Trigonometric ratios at; brainly.com/question/10167729

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