Chapter 9 Review.

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Presentation transcript:

Chapter 9 Review

Can you solve it? Name 10 body parts that contain exactly 3 letters. Example: “pit” doesn’t count

Polar Coordinates (𝑟, 𝜃) Plot the following points (5, 5𝜋 3 ) 2, − 𝜋 4 (5, 5𝜋 3 ) 2, − 𝜋 4 (1, 3𝜋)

Converting from one to the other… Polar to Rectangular 𝑥=𝑟𝑐𝑜𝑠 𝜃 and 𝑦=𝑟𝑠𝑖𝑛 𝜃 Convert (4, 30°) Rectangular to Polar 𝑟 2 = 𝑥 2 + 𝑦 2 tan 𝜃= 𝑦 𝑥 Convert (5, 5).

Equation Form Convert from Polar to Rectangular 𝑟=6 cos 𝜃 Convert from Rectangular to Polar 4𝑥𝑦=9

Graphing Polar Equations Graph: r = 3 Graph: 𝜃= 𝜋 4 Graph: 𝑟=4𝑟 sin 𝜃

Vectors 𝑃𝑜𝑖𝑛𝑡𝑠 2,4 𝑎𝑛𝑑 5, 3 Find the position vector 𝑣 using the points above. If 𝑤=<4, 4>, Solve the following: Graph 𝑣 𝑎𝑛𝑑 𝑤 Graph 𝑣+𝑤. Calculate its value. What is 3𝑣? Magnitude of 𝑣 Unit vector of 𝑣

Dot Product If 𝑣= <2, −5>𝑎𝑛𝑑 𝑤= <6, 4> Find the dot product of 𝑣 𝑎𝑛𝑑 𝑤 Find the angle between 𝑣 𝑎𝑛𝑑 𝑤 When are vectors parallel ℎ= <−2, 7> and 𝑗= <2, −7> When are vectors perpendicular The dot product is equal to zero.

Vectors 𝑃𝑜𝑖𝑛𝑡𝑠 2,4, 1 𝑎𝑛𝑑 5, 3, 2 Find the distance between the two points above. Find the position vector 𝑣 using the points above. If 𝑤=<4, 4, 3>, Solve the following: Calculate 𝑣+𝑤. What is 2𝑣? Magnitude of 𝑣 Unit vector of 𝑣

Homework - Review Pg. 632, 1-19 (odd), 51-79 (odd), 85-91(odd)