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Prerequisite Skills

Prerequisite Skills. Curtis, Chris, Camil. Properties of Exponents. Product rule a n a m = a n+m Ex. 5 2 5 3 =5 5 Quotient rule a n /a m =a n-m Ex. 5 5 /5 2 =5 3 Power rule (a n ) m = a nm Ex. (9 3 ) 2 =9 6. Negative exponents a -n =1/a n Ex. 4 -3 =1/4 3. Rational exponents

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Prerequisite Skills

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  1. Prerequisite Skills Curtis, Chris, Camil

  2. 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

  3. Properties of Logarithms • Product Rule • logan + logam = loganm • Ex. Log28 + log232 = log2256 • Power of a log • alogam(n) = m • Ex. 9log9(10) = 10 • Base Law • logaam= m • log9910 = 10 • Quotient Rule • logan – logam = loga(n/m) • Ex. Log2256 – log232 = log28 • Power Rule • nlogam = logamn • Ex. 3log28 = log2512

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

  5. The Exponential Function y=2x • 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 Ex. The value of a section of land costs $30000 and it’s value is expected to increase by 15% every 2 years.

  6. The logarithmic Function • The inverse of y=bx is • x=by Or • logbx=y (logarithmic function) y=2x y=log2x

  7. Trigonometric Ratios Special Triangles: y=sinx y=cosx y=tanx

  8. 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 radians 60° = = • Converting radians to degrees: • Ex. radians to degrees • ()x() • = • =240°

  9. 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=

  10. C.A.S.T Rule π/2 π 2π or 0 C

  11. Examples of finding exact values Find the exact values between 0 and 2π 3sinx = sinx+1 2sinx = 1 sinx= x = or tanx = -tanx = x= -

  12. Transformations of graphs • Base sine graph: y=acos(bx+c)+q / y=asin(bx+c)+q Where 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  .

  13. Problem solving • Identify values and what they do: y = 2cosx y = cos(x+1) y = -sinx y = sin(2x+6)-3 Ex. 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.

  14. 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(

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