Warm Up – 1/2 - Thursday.

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Presentation transcript:

Warm Up – 1/2 - Thursday

Warm Up – 1/2 - Thursday

1. Graphs of sin, cos, tan, and their inverses. 2. Trig Identities Today’s Exam Topics 1. Graphs of sin, cos, tan, and their inverses. 2. Trig Identities 3. Law of Sines and Cosines

Exam on Thursday Trig Review

Trig Identities csc 𝜃= 1 𝑠𝑖𝑛𝜃 sec 𝜃= 1 cos 𝜃 cot 𝜃 = 1 tan 𝜃 tan 𝜃 = sin 𝜃 cos 𝜃 cot 𝜃 = cos 𝜃 sin 𝜃 Pythagorean Identities: sin 2 𝜃+ cos 2 𝜃 =1

Examples

Law of Sines and Cosines sin 𝐴 𝑎 = sin 𝐵 𝑏 = sin 𝐶 𝑐 Law of Cosines 𝑐 2 = 𝑎 2 + 𝑏 2 −2𝑎𝑏 cos 𝐶

Law of Sines or Cosines?

Warm Up – 1/3 - Friday

Warm Up – 1/3 - Friday

Exam Review Trig Concepts Converting from Degrees to Radians and vice versa. Solving trig equations with multiple answers. Applied Story problems with angles of elevation and depression Trig Identities Law of Sine and Law of Cosines

Exam Review Polynomials General Sketches of polynomials. State the roots of a polynomial given an equation. Use the rational root theorem to find the zeroes of a polynomial.

Exam Review Rational Functions Find vertical asymptotes, horizontal asymptotes, zeroes, and holes. VA: Denominator = 0 HA: Degree of numerator vs. Denominator Zeroes: Numerator = 0 Holes: Root in both the numerator and denominator.

Exam Review Exponentials and Logarithms Solve equations involving exponential and logarithmic functions. Simplify exponential expressions involving exponents. 𝐴= 𝐴 0 1+𝑟 𝑡 𝐴= 𝐴 0 𝑏 𝑡/𝑘

Exam Review Polar Coordinates Convert from polar equations to rectangular. 𝑥=𝑟𝑐𝑜𝑠𝜃 𝑦=𝑟𝑠𝑖𝑛𝜃 Convert from rectangular to polar. 𝑟= 𝑥 2 + 𝑦 2 𝜃= tan −1 𝑦 𝑥

Exam Review Parametric Equations Eliminate a parameter and put parametric equations into rectangular form. Sequences and Series Arithmetic, Geometric, or neither Write a recursive equation for a given sequence. Summation Notation Find the sum of a finite or infinite series.

Exam Review Limits Evaluate limits algebraically. State the limit at a certain point given the graph. Right-hand limits Left-hand limits