What I Need to Know from Trig

[the stuff I was supposed to have learned last year]

[By the way, you’ll need to be able to do this WITHOUT a calculator!]

Note: AP Calculus AB never uses degrees – only radians

0° = 0 90° =

30° = 180° = Opposite Hypotenuse

45° = 270° =

60° = 360° = 2 Adjacent

In AP Calculus you should memorize the six trig function values above.

Right Triangle SOHCAHTOA

sin = cos= tan =

csc = sec= cot =

Circular Functions

(x,y) (cos, sin)

sin = csc = rr

cos = sec = ( -1, 0) (1, 0) (1, 0)

tan= cot=

1 radian 57.3°

1.57

3.14 6.28

The most important trig formula: sin2 cos 2

from which we can deriveother useful trig formulas.

(Divide all parts by sin2andwe get 1 + cot2csc2

(Divide all parts by cos2) and we get tan2 + 1 = sec2

II I

S A

T C

III IV

Trig Graphs

Special Right Triangles

In the AP-world, the answer does not need to be rationalized (Hooray!). It is sometimes easier (at least for me) to recall trig values using triangles rather than using the unit circle.

1 2 1

1

Inverse trig functions

sin-1 = arcsin ---- means the arc (or angle) whose sine is equal to some given value.

For example: sin-1 = means

INVERSE FUNCTIONS ARE NOT RECIPROCALS!!!

What I Need to Know from Pre Calculus

Linear equations:

slope-intercept form:

point-slope form:

Parallel lines have equal slopes (except vertical lines which have undefined slopes)

Perpendicular lines have slopes whose product is –1 (opposite reciprocals)

slope = =

Distance formulas:

from point to :

from point to line:

Domain and Range: Interval Notation

1x1 can be written as [ -1, 1] 1x1 can be written as 1,1 

1x1 can be written as (1,1] 1x1 can be written as [1,1)

Closed bracket is inclusive, open parenthesis is exclusive.

Always use ( ) whenever is involved.

Consider the following function:

f(x) = x2

Domain: ,

Range: [0,)

Geometry formulas:

AreaTriangle: Trapezoid: Circle:

Surface areaSphere: Lateral area of cylinder:

VolumeCone: Sphere: Cylinder:

Prism: where is the area of the base

Pyramid: where is the area of the base

Symmetry of functions:

Even functions have the property , the graph of an even function is symmetric with respect to the y-axis

Odd functions have the property , the graph of an odd function is symmetric with respect to the origin.

Zeros of polynomials:

The solutions to are

If is a polynomial with leading coefficient a and constant term c, then any rational zeros must be of the form where p is a divisor of c and q is a divisor of a.

Exponents and logarithms:

A.

B.

C.

D.If or if , then

E. and

F. and

G.

Transformations of graphs:

A. is the graph of shifted horizontally units (to the right if and to the left if )

B.is the graph of shifted vertically units (up if and down if )

C.is the graph of stretched or shrunk vertically by a factor of (stretched if and shrunk if )

D.is the graph of stretched or shrunk horizontally by a factor of (stretched if and shrunk if )

E.is the graph of reflected over the x-axis

F. is the graph of reflected over the y-axis

Sequences and series:

Arithmetic: ; ;

Geometric: ; ; ;

Special products and factoring

Sum/difference of two cubes:

Basic graphs:

, n even , n odd

,