ACP Trig Final

Degrees to radians conversion

Multiply degrees by π/180.

Arc Length Formula

s=rθ (in radians)

Area of a sector formula

A=1/2r^2(θ)

Note: circumference

For circumference the arc length is a whole circle (2-pi-r)

Note: Trig values

Sin=y/r Csc=r/y

Cos=x/r Sec=r/x

Tan=y/x Cot=x/y

Special Right Triangles

45-45-90 a•a•a(sqrt)2

30-60-90 a•2a•a(sqrt)3

Pythagorean Identities

sin^2x+cos^2x=1

1+tan^2x=sec^2x

1+cot^2x=csc^2x

Even and Odd Trig Functions

Cos and Sec are even

Sin, tan, csc, and cot are odd

Note:

Always remember:

Cosine are the x values

Sine are the y values

Quadrant Angles

0, 90, 180, 270, 360

pi/2, pi, 3pi/2, 2pi

Sin cycle and Cos cycle

Sine goes from a midline-to a peak-to a valley.

Cosine goes from a peak-to a midline-to a valley.

Standard formula for sine graph

y=aSin(bx-c) (+d)

where a is the amplitude, b is the period, and d is the midline (if present)

How to solve for each value in a sine/cosine graph

Amp=|a|

Period=2pi/b

Step size=period/4

Phase shift/new start= set (bx-c)=0

Midline=d

[0, 2pi)

Means only look for answers that occur in the first revolution, don't add an additional rev (+2pi)

Solving a right triangle with missing values

Use Pythagorean theorem , and use values you know are 100% correct

How do you undo sine?

Use sine inverse

Equation used when solving trig equations

X1=(point/coordinate)+2pi n

Note: solving trig equations

1. Factor first (set =)

2. Find zeros

3. Plot angle on unit circle

4. Write down your solutions

Note: using double angle formulas

Step 1: find quadrant

Step 2: draw out triangle and find values (using Pythagorean theorem)

Step 3: plug them in and use double angle formulas

Note: when using sum to product formula...

Do not solve out like a regular subtraction/addition problem

Use the formula

What does finding exact value mean?

Exact value means no calculator

sin inverse is..

Y in restriction

Also the positive vertical

Cosine inverse is...

The positive horizontal

What is the restriction of tan?

Tan inverse is the same as sine inverse

Note: sine inverse problem

Example:

Sin(arccos-2/3)

The arccos is the angle, and no pi means we use x/r to find the values on the right triangle on unit circle. (X=-2, Y=sqrt 5, r=3)

law of sines formula

sinA/a = sinB/b = sinC/c

Use when you have an angle side pair

Law of cosines formulas

a² = b² + c² - 2bcCosA

b² = a² + c² - 2acCosB

c² = a² + b² - 2abCosC

Definition of the magnitude of a vector

||a||= ||

Definition of Addition of Vectors

Definition of a Scalar Multiple of a Vector

m

Definition of 0 and -a

0=<0,0> and -a= -

Definition of Subtraction of Vectors

a-b =

Definition of i and j

i=<1,0> j=<0,1>

(I goes 1 right)

(J goes 1 up)

i, j form for vectors

a =

Formulas for horizontal and vertical components of a =

If a vector and the angle (theta) are defined as above, then

a1= ||a|| cos (theta)

and

a1= ||a|| sin (theta)

Note: Always remember...

Math is about shape and form.

If you can't find the answer in the current form, draw a picture and change the form.