Prerequisite SkillsCurtis, Chris, Camil

Properties of Exponents

Product rule anam=an+m Ex. 5253=55

Quotient rule an/am=an-m Ex. 55/52=53

Power rule (an)m=anm Ex. (93)2=96

Negative exponents a-n=1/an Ex. 4-3=1/43

Rational exponents an/m=man Ex. 52/3=52

Properties of Logarithms

Power of a log alogam(n) = m Ex. 9log9(10) = 10

Base Law logaam = m log9910 = 10

Product Rule logan + logam = loganm Ex. Log28 + log232 = log2256

Quotient Rule logan – logam = loga(n/m) Ex. Log2256 – log232 = log28 Power Rule nlogam = logamn Ex. 3log28 = log2512

Converting

The exponential function an=y can be expressed in logarithmic form as logay=n Ex. 43=64 (exponential) log464=3 (logarithmic) Ex. log12144=2 (logarithmic) 122=144 (exponential)

The Exponential Function y=bx

The base b is positive and b cannot equal 1 The y-intercept is y=1 Horizontal asymptote at the x-axis The domain is any real value of x The range is all positive values The function is increasing when b The function is decreasing when 0

y=2x

Ex. The value of a section of land costs $30000 and it’s value is expected to increase by 15% every 2 years.

The logarithmic Function

The inverse of y=bx is x=by

Or logbx=y (logarithmic function)

y=2x

y=log2x

Trigonometric RatiosSpecial Triangles:

y=sinx y=cosx y=tanx

Radian Measure

A radian is an arc of a circle that is equal to the radius r=180°Converting degrees to radians:

Ex. 60° to radians60°== 

Converting radians to degrees: Ex. radians to degrees()x()==240°    

SYR CXR TYX & SOH CAH TOA

When solving for the value of a trigonometric ratio these following rules are needed: sinΘ= cosΘ= tanΘ=When solving for a trig ratio within a circle:sinΘ= cosΘ= tanΘ=

C.A.S.T Rule

All Ratios (+)Cos (+)Tan (+)4th Qtr

AS

T C

π/2

π

3π2

2π or 0

Examples of finding exact values

Find the exact values between 0 and 2π 3sinx = sinx+1 2sinx = 1 sinx = x = or tanx = -tanx = x= -

Transformations of graphs Base sine graph: y=acos(bx+c)+q / y=asin(bx+c)+qWhere A= 1 B= 1 C= 0 The A value controls the vertical stretch or compression. If the A value is greater than one, then the base graph is stretched by a factor of A. If the value is less than one, then it is compressed by a factor of A. The A value is known as the amplitude.The B value controls the horizontal stretch. If the value is less than one, then you stretch by a factor of the denominator. If It is greater than one, you compress by a factor of the value.The C value is responsible for the phase shift left/right on the horizontal plane. If the value is negative, you move the graph to the right, and if it is positive, you move to the left.The Q value is responsible for the vertical shift on the graph. Move up or down by the corresponding value.The value B is the number of cycles it completes in an interval of 0 to .The value B affects the period. The period of sine and cosine is  .

Problem solving Identify values and what they do: y = 2cosxy = cos(x+1)y = -sinxy = sin(2x+6)-3Ex. The price of snowboards fluctuates between a maximum of $150 and a minimum of $100 over a year. The peak selling time is in January (t=0) and the slowest time is in July (t=6). Sketch the graph.

Trig Identities

Reciprocal Identities csc= sec= cot =

Pythagorean Identities sin22 1 tan22 1 + cot2 = csc2

Quotient Identity tan cot

Reflection Identities sin(- cos(-

Cofunction Identities cos( sin(