How would you find the exact value of the six trigonometric function of pi/3?

1 Answer
Alan P.
Sep 9, 2016

(see below)

Explanation:

Consider an equilateral triangle with sides of length 2;
each of an equilateral triangle has an angle of pi/3
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The altitude of the triangle divides the base into two equal length segments; each with a length of 1.

Using the Pythagorean Theorem, we can find that the height of the triangle is sqrt(3)

Considering only one side of the equilateral triangle and the basic trigonometric definitions:

sin(theta)="opposite"/"hypotenuse" rarr sin(pi/3)=sqrt(3)/2

cos(theta)+"adjacent"/"hypotenuse" rarr cos(pi/3)=1/2

tan(theta)="opposite"/"adjacent" rarr tan(pi/3)=sqrt(3)

csc(theta) ="hypontenuse"/"opposite" rarr csc(pi/3)=2/sqrt(3)=(2sqrt(3))/3

sec(theta)="hypotenuse"/"adjacent" rarr sec(pi/3)=2

cot(theta)="adjacent"/"opposite" rarr cot(pi/3)1/sqrt(3)=sqrt(3)/3

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