Math Midterm

Question 1

Arc Length

Answer 1

S = r * θ

Question 2

Area of Sector

Answer 2

1/2 * θ * r^2

Question 3

Linear Speed

Answer 3

V = s/t

Question 4

Angular Speed Formula

Answer 4

w = θ/t

Question 5

Linear speed using angular speed

Answer 5

V = r*w

Question 6

Law of Sines

Answer 6

Sin A/a = sin B/b

Question 7

Law of Cosines

Answer 7

a^2 = b^2 + c^2 - 2bc * cos(A)

Question 8

Periodic Function

Answer 8

f(x) = a * sin or cos bx

Question 9

Amplitude

Answer 9

|a|

No amplitude for tan functions (undefined)

Question 10

Period

Answer 10

Sin: 2pi/|b|
Cos: 2pi/|b|
Tan: Pi/|b|
Csc: 2pi
Sec: 2pi
Cot: Pi

Question 11

sin(sin^-1 x) = x

Answer 11

-1 ≤ x ≤ 1

Question 12

cos(cos^-1 x) = x

Answer 12

-1 ≤ x ≤ 1

Question 13

tan(tan^-1 x) = x

Answer 13

-∞ < x < ∞

Question 14

sin^-1(sin x) = x

Answer 14

-pi/2 ≤ x ≤ pi/2

Question 15

cos^-1(cos x) = x

Answer 15

0 ≤ x ≤ pi

Question 16

tan^-1(tan x) = x

Answer 16

-pi/2 < x < pi/2

Question 17

sin θ

Answer 17

y

Question 18

cos θ

Answer 18

x

Question 19

tan θ

Answer 19

y/x

Question 20

csc θ

Answer 20

1/y

Question 21

sec θ

Answer 21

1/x

Question 22

cot θ

Answer 22

x/y

Question 23

What will you remember?

Answer 23

When to switch from radians and degrees mode

Question 24

Positive Trigonometric Values

Answer 24

Quad I: All
Quad II: sin, csc
Quad III: tan, cot
Quad IV: cos, sec

Question 25

S

Answer 25

S = r * revolutions * 2pi

Question 26

θ

Answer 26

2pi*revolutions

Question 27

Area of triangle using sin

Answer 27

A = 1/2 BCsin(angle in between)

Question 28

Heron’s Formula

Answer 28

s = (a + b + c)/2
A = sqrt(s*(s-a)(s-b)(s-c))