Law of Sines
State the Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
State the Law of Cosines
a2=b2+c2-2bc cosA
b2=a2+c2-2ac cosB
c2=a2+b2-2ab cosC
Convert the polar equation r=4 to a rectangular equation in x and y:
42=x2+y2
What is i² equal to?
-1
What is a vector?
A quantity with magnitude and direction
Solve the triangle with A=64*,C=82*,and c=14 centimeters. Round lengths of sides to the nearest tenth.
a=12.7 cm
b=7.9 cm
In triangle ABC, b=10,c=10, and angleA=60*. Find the length of side a.
a=10
To convert a point from polar coordinates (r, theta) to rectangular coordinates (x,y), use the formulas:
x= r cos theta and y= r sin theta
What is the polar form of a complex number?
r(cosθ + i sinθ)
Find ⟨1, 2⟩ • ⟨2, 1⟩.
4
Solve the triangle ABC if A=40*, C=22.5*, and b=12. Round the measures to the nearest tenth.
a=8.7
c=5.2
Find the measure of angleA if the sides of the triangle are a=7, b=5, and c=8.
angleA= 60*
Convert (−2, π/3) to an equivalent positive r form.
(2, 4π/3)
Write 5(cosπ+isinπ) in standard form.
−5+0i
Find the magnitude of ⟨3, 4⟩.
5
Find the measure of angleB in a triangle where a= 7, b=16, and A=30*.
No solution
If angleC=90*, the law of cosines (c2=a2+b2-2ab cosC) simplifies into which famous geometric theorem?
The Pythagorean Theorem
What shape is r = 2cos(θ)?
Circle
Write cos(0)+isin(0) in standard form.
1
Find the dot product: ⟨1, 2⟩ • ⟨3, 4⟩
11
Solve for all possible measures of angleB given a triangle where a=12, b=15, and A=40*
There are two possible solutions
B is approximately 53.5* or
B is approximately 126.5*
To use the Law of Cosines to solve a triangle, you must be given which two specific "case" combinations of sides and angles?
SAS and SSS
What shape is r = 1 + cos(θ)?
Cardioid
Using DeMoivre’s Theorem, what is (cosθ+isinθ)^2?
cos(2θ)+isin(2θ)
What does it mean if the dot product of two vectors is 0?
They are perpendicular