MAT170 SPR 2009 Material for 3rd Quiz. Sum and Difference Identities: ( sin ) sin (a + b) = sin(a)cos(b) + cos(a)sin(b) sin (a - b) = sin(a)cos(b) - cos(a)sin(b)

MAT170 SPR 2009 Material for 3rd Quiz

Sum and Difference Identities:(sin)

sin (a + b) = sin(a)cos(b) + cos(a)sin(b)

sin (a - b) = sin(a)cos(b) - cos(a)sin(b)

Sum and Difference Identities:(cos )

cos (a + b) = sin(a)sin(b) - cos(a)cos(b)

cos (a - b) = sin(a)sin(b) + cos(a)cos(b)

Pythagorean Identities

Reciprocal Identities

Quotient Identities

Even-Odd Identites

Functions sin & cos

Functions tan & cot

Functions sec & csc:

Which Function goes with the graph? sin

crosses the Y axisat midpoint

cos crosses the Y axis

at high (or low) point

sec and tan cross the y axis

csc and cot have asymptotes at Y

axis

How to find Coterminal Angles:

Coterminal = Given ± Coterminal = Given ± kk(2π)(2π) + if angle is negative - if angle is positive

KK ≈ Given /2π≈ Given /2π (round upup if angle is negative, round downdown if angle is positive)

Remember: 2π = 360°

Hint on finding Coterminal Angles in radians:

Coterminal = Coterminal = ΘΘ ± ± kk(2π)(2π) + if angle is negative - if angle is positive

Convert Convert 2π 2π to match to match denominators with denominators with ΘΘ, then k , then k

is easy to solveis easy to solve 2π 2π == 4π/2 4π/2 == 6π/3 6π/3 == 8π/4 8π/4 == 12π/6 12π/6

How do you convert between radians and

degrees?

So by dimensional analysis:

X° (π/180 ° ) = Θ radiansAnd

Θ radians (180 °/π) = X°

Formula for length of an arc:

Θ must be in radians

Linear speed of a point on a circle:

Distance/time

Where S = RΘ

A useful mnemonic for certain values of sines and cosines

For certain simple angles, the sines and cosines take the form  for 0 ≤ n ≤ 4, which makes them easy to remember.

30º =

45º =

60º =

sin П

6.

cos П

6.

tan П

6.

2

When you remember what is underneath,

Click the shape to make certain.

.

A

B

CΘ

X = cos Θ Y = sin Θ

tan tan ΘΘ = =

X = cos Θ Y = sin Θ

cot cot ΘΘ = =

X = cos Θ Y = sin Θ

sec sec ΘΘ = =

X = cos Θ Y = sin Θ

csc csc ΘΘ = =

Trig Co-function Identities:

* Co-Function for Sine:

* Co-Function for Cosine:

* Co-Functions for Tangent:

* Co-Function for Cotangent:

* Co-Function for Secant:

* Co-Function for Cosecant:

sin a = cos (π/2 – a)

cos a = sin (π/2 – a)

tan a = cot (π/2 – a)

cot a = tan (π/2 – a)

sec a = csc (π/2 – a)

csc a = sec (π/2 – a)