AP Precalculus: Further Applications of Trigonometry flashcards

Question 1

What is an oblique triangle?

Accepted Answer

A triangle with no right angle

Question 2

What is the ambiguous case in solving triangles?

Accepted Answer

An oblique SSA setup that more than one triangle can satisfy

Question 3

How many solutions can an SSA triangle have?

Accepted Answer

One, two, or none

Question 4

What does the Law of Sines say?

Accepted Answer

sin α/a = sin β/b = sin γ/c

Question 5

State the Law of Cosines for side a opposite angle α.

Accepted Answer

a^2 = b^2 + c^2 − 2bc cos α

Question 6

What is the area of a triangle with sides b and c and included angle α?

Accepted Answer

Area = (1/2)bc sin α

Question 7

State Heron's formula for the area of a triangle with sides a, b, c.

Accepted Answer

Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c)/2

Question 8

What is the pole in a polar grid?

Accepted Answer

The origin of the polar grid

Question 9

How do you convert polar (r, θ) to rectangular x and y?

Accepted Answer

x = r cos θ and y = r sin θ

Question 10

How is r related to rectangular x and y?

Accepted Answer

r^2 = x^2 + y^2

Question 11

For r = a ± b cos θ, what ratio a/b gives a cardioid?

Accepted Answer

a/b = 1

Question 12

For r = a ± b cos θ, what condition gives an inner-loop limaçon?

Accepted Answer

a < b

Question 13

For r = a ± b cos θ, what range of a/b gives a dimpled limaçon?

Accepted Answer

1 < a/b < 2

Question 14

How many petals does the rose r = a cos nθ have when n is even?

Accepted Answer

2n petals

Question 15

How many petals does the rose r = a sin nθ have when n is odd?

Accepted Answer

n petals

Question 16

What is the argument of a complex number?

Accepted Answer

The angle between the positive real axis and the line from the origin to the number's point

Question 17

What is the modulus |z| of z = a + bi?

Accepted Answer

|z| = √(a^2 + b^2)

Question 18

How is a complex number z written in polar form?

Accepted Answer

z = r(cos θ + i sin θ)

Question 19

How do you multiply two complex numbers in polar form?

Accepted Answer

Multiply their moduli and add their angles

Question 20

How do you divide two complex numbers in polar form?

Accepted Answer

Divide their moduli and subtract their angles

Question 21

By De Moivre's Theorem, how is z^n found for a positive integer n?

Accepted Answer

Raise the modulus to the nth power and multiply the angle by n

Question 22

In parametric equations, what is the parameter?

Accepted Answer

A variable, often time, on which both x and y depend

Question 23

What is a scalar?

Accepted Answer

A quantity with magnitude but no direction

Question 24

What is a vector?

Accepted Answer

A quantity with both magnitude and direction, drawn as a directed line segment

Question 25

What is the dot product of two vectors?

Accepted Answer

The product of their horizontal components plus the product of their vertical components

Question 26

How do you find the unit vector in the direction of a nonzero vector v?

Accepted Answer

Divide v by its magnitude

AP Precalculus: Further Applications of Trigonometry flashcards

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