12-04: Trigonometry

LS

Trig identities: both ________ and RS should be equal.

hard disk of a personal computer

The ________ rotates at 7200 RPM.

Radian

measure of an angle formed by rotating the radius of the circle through an arc length equal to the radius

It is a unit of measurement

rads for short

you can use fractions of semi circles to find other values

what you do to one side you must do to the other

Exact

leave π and fractions

Approximate

decimal value

RPM

Revolutions per minute → revolutions divided by minutes

with non-special angles

note that this only can be used with the benchmarks that are labelled below

Equivalent expressions

expressions that yield the same value for all values of the variable

Sine <

> COsine

Secant <

> COsecant

Tangent <

> COtangent

Compound angle expression

Trig expression that depends on 2 or more angles

cos(x+y)= cosxcosy

sinxsiny

sin(x-y)= sinxcosy

cosxsiny

Trig identities

both LS and RS should be equal

radian

measure of an angle formed by rotating the radius of the circle through an arc length = to the radius, unit of measurement (rads)

radian measure of an angle ϴ

ϴ =(a/r)

conversions between deg and rads

180º = π rads

angular velocity

rate of change, how much does the angle change. factor label method process is used to change units - it is a ratio

rule of co

sine

steps for determining equivalent trig expressions using cofunction identities

1. is the angle q1 or q2; 2. find the correlated angle; 3. rule of co for ratio

compound angle formulas: cos(x-y)

cosxcosy + sinxsiny

compound angle formulas: cos(x+y)

cosxcosy - sinxsiny

compound angle formulas: sin(x-y)

sinxcosy - cosxsiny

compound angle formulas: sin(x+y)

sinxcosy+cosxsiny

trig identities

“Prove” tells you to do trig identities

• Split LS and RS

• No rearranging

• No skipping steps

• Replace everything with sin and cos

• Simplify each side