preCalc 5-3...
15
preCalc_53_trigIdentities.notebook 1 November 02, 2011 Nov 18:06 AM Who am I? Nov 18:08 AM Warm Up 1) Solve: 2) Consider the point Q on the graph of y = 2x 3 +3. Find the point Q such that it is closest to the point (1, 1). Q = (0.934, 1.370)
Transcript of preCalc 5-3...
preCalc_53_trigIdentities.notebook
1
November 02, 2011
Nov 18:06 AM
Who am I?
Nov 18:08 AM
Warm Up
1) Solve:
2) Consider the point Q on the graph ofy = 2x3 + 3. Find the point Q such that it is closest to the point (1, 1).
Q = (0.934, 1.370)
preCalc_53_trigIdentities.notebook
2
November 02, 2011
Nov 18:18 AM
Nov 18:18 AM
2) Consider the point Q on the graph ofy = 2x3 + 3. Find the point Q such that it is closest to the point (1, 1).
X= .934Y= 1.969
Q = (0.934, 1.370)
y = 2(0.934)3 + 3
Point Q on y = 2x3 + 3
preCalc_53_trigIdentities.notebook
3
November 02, 2011
Nov 18:20 AM
Answers to Evens2) sinθ= √3/2 cscθ= (2√3)/3
cosθ= 1/2 secθ= 2tanθ= √3 cotθ= √3/3
4) sinθ= (2√6)/5 cscθ= (5√6)/12cosθ= 1/5 secθ= 5tanθ= (2√6) cotθ= √6/12
8) sinθ= 2/3 cscθ= 3/2cosθ= √5/3 secθ= (3√5)/5tanθ= (2√5)/5 cotθ= √5/2
6) sinθ= √2/2 cscθ= √2cosθ= √2/2 secθ= √2tanθ= 1 cotθ= 1
10) 1
12) 0
14) 1
16) 0
18) 0
Nov 211:45 AM
preCalc_53_trigIdentities.notebook
4
November 02, 2011
Nov 211:46 AM
Nov 211:48 AM
preCalc_53_trigIdentities.notebook
5
November 02, 2011
Nov 18:20 AM
InterplayWith
Trig Functions
Nov 18:25 AM
The Period of Trig Functions
Fact: All trig functions repeat every 2π
Consider: sin(θ) = x
Believe: sin(θ + 2π) = x
How about: sin(θ + 6π) = ?
How about: sin(θ + 9π) = ?
preCalc_53_trigIdentities.notebook
6
November 02, 2011
Nov 18:25 AM
The Period of Trig Functions
Fact: The tangent and cotangent functionsrepeat every π
Consider: tan(θ) = x
Believe: tan(θ + π) = x
How about: tan(θ + 6π) = ?
How about: tan(θ + 9π) = ?
Nov 18:28 AM
Ex 1 Evaluating CoTerminal Angles
preCalc_53_trigIdentities.notebook
7
November 02, 2011
Nov 18:28 AM
Ex 2 Evaluating CoTerminal Angles
Nov 18:28 AM
Ex 3 Evaluating CoTerminal Angles
preCalc_53_trigIdentities.notebook
8
November 02, 2011
Nov 18:28 AM
Ex You Try Evaluating CoTerminal Angles
1)
2)
Nov 18:36 AM
The Signs of Trig Functions
All Students Take Calculus
Note:• A = all 6 functions• S = sine and cosecant• T = tangent and cotangent• C = cosine and secant
preCalc_53_trigIdentities.notebook
9
November 02, 2011
Nov 18:41 AM
The Interplay
Nov 18:47 AM
Interplay Practice Ex 1
Given: &
Define all 4 remaining trig function.
preCalc_53_trigIdentities.notebook
10
November 02, 2011
Nov 18:47 AM
Interplay Practice Ex 2
Given: &
Define all 4 remaining trig function.
Nov 18:47 AM
Interplay Practice You Try
Given: &
Define all 4 remaining trig function.
preCalc_53_trigIdentities.notebook
11
November 02, 2011
Nov 19:06 AM
The Three Main Identities"Big Mama"
"The Kids"
NOTE:
Nov 19:11 AM
The Circle Begat Mama
Definition of a circle:
Unit circle definition:
We can easily see the substitutions made
preCalc_53_trigIdentities.notebook
12
November 02, 2011
Nov 19:18 AM
Mama Begat The Kids
Nov 19:18 AM
Mama Begat The Kids
preCalc_53_trigIdentities.notebook
13
November 02, 2011
Nov 19:20 AM
Using Identities to Evaluate Ex 1
Nov 19:20 AM
Using Identities to Evaluate Ex 2
preCalc_53_trigIdentities.notebook
14
November 02, 2011
Nov 112:32 PM
Odd/Even Trigerry
Sine, Cosecant, Tangent and Cotangent are all odd functions
Cosine and Secant are both even functions
Nov 112:32 PM
Odd/Even Trigerry Ex 1
preCalc_53_trigIdentities.notebook
15
November 02, 2011
Nov 112:32 PM
Odd/Even Trigerry Ex 2
Nov 112:34 PM
Assignmentp 411
#s: 1 32 Odd#s: 67 78 All
