3 4 Fundamental Trigonometric Identities Mrs Lisa Allen
- Slides: 18
(3 -4) Fundamental Trigonometric Identities Mrs. Lisa Allen Honors Pre-calculus Saucon Valley High School
Old Familiar Identities n 2+3=3+2 n 6(x) = x(6) n n Commutative Property Addition Commutative Property Multiplication (½ + 3/2) + 3 = ½ + (3/2 + 3) Associative Property of Addition 4 – 3 = 4 + -3 Definition of Subtraction
Definition: Trigonometric Identities n n A trigonometric identity is a trigonometric equation that is true for all values. Reciprocal Identities from Chapter 1 include:
Chapter 1 Basic Trigonometry Review
Example 1 Prove: sec cos = 1 (1) Given (2) Reciprocal Identities (3) Simplification (4) Simplification
Prove Ratio (or Quotient) Identities n Example 2: Prove (1) Prove: (2) Definition of sine and cosine (3) Simplification of a complex fraction (4) Definition of cotangent OR And
Example 3 Prove sin = tan cos sin tan cos (1) Prove this is so! (2) Definition of tangent and cosine (3) Simplification (4) Simplification (5) Definition of sine
!Notation!
Example 4 Prove: 1 (1) PROVE (2) DEFN: SINE & COSINE (3) POWER OF A QUOTIENT RULE (4) ADDITION OF TWO FRACTIONS (5) UNIT CIRCLE PYTHAGOREAN TRIPLE x, y, AND r (6) SIMPLIFICATION 1=
Quotient Identities Pythagorean Identities
Unit Circle P(x, y) r x y
Pythagorean Identities n n n There are three of these, but memorization of the first one will help with the other two. We have already proved this one. So, in the next part we’ll try to derive the other two Pythagorean identities
Pythagorean Identity #2 BEGIN WITH PYTHAGOREAN #1 We HAVE WORKED WITH THE RATIO IDENTITIES…so…. DIVIDE EACH TERM BY sine squared SIMPLIFICATION
Pythagorean Identity #2 BEGIN WITH PYTHAGOREAN #1 Again using the RATIO IDENTITIES DIVIDE EACH TERM BY cosine squared SIMPLIFICATION
Even and Odd Identities Odd Function Even Function Odd Function
Prove: y P(x, y) tan(- ) -tan r x - r -tan P(x, -y)
Example 6: Verify the following identities for = 45 a) b) Verifying uses specific values
Homework assignment n P. 133 #s 3 -30 (multiples of 3) #37 & #38
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- Fundamental trig identities
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- Basic identities
- Differentiation of trigonometry
- 5-2 verifying trigonometric identities
- Lesson 11 transforming the graph of the sine function
- 5-2 verifying trigonometric identities
- Two quotient identities
- Trigonometric identities
- Sin 60
- Chapter 7 trigonometric identities and equations answer key
- Trigonometric identities grade 11
- Cos90
- 1+tanx^2
- Trig identities quotient
- 5-1 trigonometric identities
- Cot2x identity