Trigonometry: Finding the value of sine Pi/3.

Trigonometry: Finding the value of sine Pi/3.

First we need to remember that the whole circle is 360° and in radians it is 2Pi. So then Pi is 180°, and Pi/3 is 60°.

To find sine of Pi/3, you'd want to have a right triangle with one angle 60°.

Fortunately that is easy to come by; just take an equilateral triangle and draw an altitude to it. You will have two identical 30°-60°-90° triangles.

And yes this is one of the special triangles - also used in drafting, and there are rulers in this shape.



Where on this picture is the 60° angle? Where's the 30° angle?


Now, to get sine 60° one needs side lengths. I made the sides of this equilateral triangle ABC to be 2 units. The side CD is obviously just 1 unit (easy numbers thus far!)

But what about the height h?

Well, that's where we need to dig up the goold ole' Pythagoras. Can't forget him.

You write the equation, h² + 1² = 2²

h² = 2² − 1² = 3.

So taking square roots... h = √3.

Then, to the sine.

Remember sine is a ratio of side lengths; it is the ratio of the OPPOSITE side to the hypotenuse.

....and soon you will have the answer: sine 60° is _____ (fill in the blank.)

So it was easy, just using the very basics of trigonometry.

However, I wouldn't memorize the result. Just remember the idea HOW it was derived; and you can derive it when you need it (such as in a test).

Read also:
Special Right Triangles