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mttal24

Member

Registered: 2012-05-01

Posts: 23

Trignometric functions and ratios for any angle

I have read all basics of trignometry and  I have a question:
Find 

and

I have read all the questions related to these on mathsisfun.com but all the questions there are like sin 330 is given and a related acute angle's value is given.
But how do I convert this into an acute angle?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Trignometric functions and ratios for any angle

hi mttal24

The usual definition for sin / cos over 90 degrees is to rotate a point around the origin and specify it's coordinates as (cos angle, sin angle).

To make this work the distance from origin to the point must be one unit.  Then this definition works for 0 - 90 as well.

So sketch a pair of axes, mark where a 330 rotation would place the point and then consider what size its y cooordinate must be.

Look at my diagram.

The line OA has rotated 330 degrees from the positive x axis.

By symmetry I can see that CA = CB (but below the axis and therefore negative).

The angle BOC = 30 degrees.

So sin 330 = minus sin 30 = -0.5

To do -420 I would keep adding 360 until the angle is positive. (sin is a periodic function, repeating every 360)

So -420 --> -60 --> +300

Now I've got an angle I can work with.

sin -420 = sin -60 = sin 300 = minus sin 60 = -√3 / 2

As a general tip sine is positive from 0 - 180 and negative from 180 - 360.

Cosine is positive from 0 - 90 and again from 270 - 360.

There's a brilliant interactive tool made by MIF for this at

http://www.mathsisfun.com/geometry/unit-circle.html

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob