You should KNOW

1. That the trig functions are intricately related by

many identities i.e. formulas that are true for all

values. When indicated, these must be MEMORIZED with

understanding. Formulas will not be provided on exams.

(Note: But you don't need everything in the books--only the

ones listed here. In most cases these can be easily

remembered and understood in graphical/geometric terms,

or can be easily deduced from others.)

2. The Pythagorean identity: **sin^2(x) + cos^2(x)=1**, how it

is related to the Pythagorean Theorem, the

identity **tan^2(x) + 1 = sec^2(x)** that can be derived

from it by dividing everything by **cos^2(x)**, and the similar

identity involving cot and csc. NOTE: **sin^2(x)** is just a

convenient way of writing **[sin(x)]^2** !

3. The odd/even identities: **cos(x)=cos(-x)**, **sin(-x)=-sin(x)**, etc.,

which can be remembered either by recalling that the

**sin** function is odd and the **cos** function is even, by the

appearance of the **sin** and **cos** graphs, or by the definitions

of **sin** and **cos** as coordinates of points on the unit circle and

the meaning of positive/negative angles.

4. The sum and difference identities for **sin(x+y)**, **cos(x+y)**.

These must simply be memorized, but these are the ONLY

identities that you really need to memorize. You can get the

others from these. For example the identity for **sin(x-y)** can

be obtained from sin(x + (-y)) and the odd/even identities.

You don't need to remember the **tan(x+y)** identity.

5. The double angle identities for sin(2x), cos(2x). These can

be easily obtained from the sum identities since

**sin(2x) = sin(x + x)**, etc. You don't need to remember the

half-angle identities.

6. The cofunction identities: e.g. sin(pi/2 - x) = cos x,

cos(pi/2 -x) = sin x, etc. These can be easily remembered by

thinking of the complementary angles in a right triangle:

The sin of one is the cosine of the other.

7. The period identities: sin(x + 2pi) = sin x, sin(x + pi) = -sin x.

(Think of the graphs of the sin and cos functions.)

You should be ABLE TO

1. Use the basic identities together with your knowledge of

algebra to simplify trigonometric expressions.

2. Make simple deductions of one identity from others, e.g.

deduce the identity for sin(2x) from the sin(x+y) identity.

3. Use trig identities to determine trig functions of angles

from other trig functions of related angles, e.g. Find

**tan x** from knowledge of **sin x**, find **sin(x+y)** from knowledge

of sin x, sin y, cos x, cos y, etc.