# Trig Identities and Working Core 2

Basic examples and working to aid your understanding towards trigonometric identities :)

The basic understanding should hopefuly give the ability to answer the more challenging questions successfully :)

Hope it helps !

- Created by: George
- Created on: 11-05-11 19:57

First 223 words of the document:

Core 2 Revision

Trigonometrical identities and simple equations

The two identities that you need to know:

Sin2 x + cos2 x = 1

Tan x = sin x / cos x

These are key to answering any kind of question as they usually involve simplifying

expressions so that they only involve one of the three functions (sin, cos and tan).

For example

2cos2 x + 9sin x = 3sin2 x

2(1 sin2 x) + 9sin x = 3sin2 x

2 2sin2 x + 9sin x = 3sin2x

5sin2 x 9sin x 2 = 0

Solving for x

Solving equations can be quite straight forward, as long as you follow the following steps.

1. Rearrange the equation so that there is only one function involved.

2. Work out your value of x

For example: sin x = ½ so x = 30

3. Draw a Cast Diagram and use it draw the value of x in each of the four quadrants.

4. If the value of sin x is positive consider the quadrants where sin is positive (the same

goes for cos and tan, if cos x is positive only consider the quadrants where cos is

positive)

If the value of sin x was negative consider the quadrants where sin is negative

5. Work out the values of x for where the function is positive.

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