Precalculus: Further Applications of Trigonometry flashcards

Question 1

What is an oblique triangle?

Accepted Answer

A triangle that is not a right triangle

Question 2

State the Law of Sines for a triangle with angles α, β, γ opposite sides a, b, c.

Accepted Answer

sin α / a = sin β / b = sin γ / c

Question 3

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

Accepted Answer

½ bc sin α

Question 4

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

Accepted Answer

a² = b² + c² − 2bc cos α

Question 5

What is Heron's formula for the area of a triangle with sides a, b, c?

Accepted Answer

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

Question 6

In the SSA case, how many triangles can the given data produce?

Accepted Answer

One, two, or none

Question 7

How do you get x and y from polar coordinates (r, θ)?

Accepted Answer

x = r cos θ and y = r sin θ

Question 8

In polar conversion, r² equals what in rectangular coordinates?

Accepted Answer

x² + y²

Question 9

In polar conversion, tan θ equals what in rectangular coordinates?

Accepted Answer

y / x

Question 10

What is the pole on a polar grid?

Accepted Answer

The origin

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

What are the polar equations of a lemniscate?

Accepted Answer

r² = a² cos 2θ or r² = a² sin 2θ, with a ≠ 0

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 modulus |z| of z = a + bi?

Accepted Answer

√(a² + b²)

Question 17

What is the polar form of a complex number z with modulus r and angle θ?

Accepted Answer

z = r(cos θ + i sin θ)

Question 18

To multiply two complex numbers in polar form, what do you do with the moduli and the angles?

Accepted Answer

Multiply the moduli and add the angles

Question 19

To divide two complex numbers in polar form, what do you do with the moduli and the angles?

Accepted Answer

Divide the moduli and subtract the angles

Question 20

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

Accepted Answer

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

Question 21

What is the argument of a complex number?

Accepted Answer

The angle a segment from the origin to the point makes with the positive real axis

Question 22

What are the unit vectors i and j in component form?

Accepted Answer

i = ⟨1, 0⟩ and j = ⟨0, 1⟩

Question 23

What is the magnitude of v = ai + bj?

Accepted Answer

|v| = √(a² + b²)

Question 24

What is the dot product of ⟨a, b⟩ and ⟨c, d⟩?

Accepted Answer

ac + bd

Question 25

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

Accepted Answer

Divide v by its magnitude |v|

Question 26

What is a scalar?

Accepted Answer

A quantity with magnitude but no direction

Question 27

What is a vector?

Accepted Answer

A quantity with both magnitude and direction

Precalculus: Further Applications of Trigonometry flashcards

The cards

Where this deck sits in the curriculum

How this deck was checked

Sources

More in this course