PreCalc/Trig Final

WB 1 - 3

100

Two angles with the same initial and terminal sides

What is Coterminal Angles

200

The Pythagorean Identity [Formula]

cos^2(x) + sin^2(x) = 1

300

f(-x) = -f(x) is....

What is an odd function?

400

sec^2(x)cos(x) = sec(x)

True or False?

True

500

A bicycle with 30-inch diameter wheels is traveling at 10 mi/h. Find the angular speed of the wheels in rad/min.

703.99999

WB 4 - 6

100

Amplitude = vertical shift 

True/false?

false

200

What is the definition of cscθ for a right triangle that has a hypotenuse of length r?

r/y

300

y=-sin(12(x-π/24))

1. Amplitude =?
2. Period = ?
3. Phase shift =?
4. Midline y= ?

1. Amplitude = 11
2. Period = π/6
3. Phase shift = −π/24
4. Midline y=0

400

y=1/16sec(x-π/2)

1. Vertical Stretching = ?

2. Period = ?

3. Phase shift = ?

4. Midline = ?

1. Vertical Stretching = 1/16

2. Period = 2π

3. Phase shift = π/2

4. Midline y=0

500

A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3261-foot mesa. In 2 minutes, the angle of depression to the leading edge of the fire changes from 10.13∘ to 12.56∘.
How many feet does the fire advance during the 2 minutes that the ranger is observing it? (whole number is ok!)

3614 / 3615

(3614.924747)

WB 7 - 9

100

sin^-1(x) = 1/sin(x)

True/false?

false

200

csc²(x) = 1 - cot²(x)

True/false?

false

correct:

csc²(x) = 1 + cot²(x)

300

Prove

sec(x) - tan(x)sin(x) = 1/sec(x)

You did great <3

400

tan^-1(-sqrt(3)/3) = ...?

-pi/6

the range of tan^-1 is π/2 to −π/2,

500

cos(x−3π/2)= ...?

−(sin(x))

WB 10 - 12

100

Trig identities that show how to find the sine, cosine, or tangent of twice a given angle.

What is Double Angle Identities

200

Law of Sines and Law of Cosines can be used on any type of triangle 

True/False

True

300

By using known trig identities, 

sin(2x)/1+cos(2x) 

can be written as...

tan(x)

400

Find all solutions of the equation tan⁵x−9tanx=0.

pi/3 or 1/3

500

 a=9.8  b=11, A=50∘

number of possible triangles:  

2

WB 13 - 15

100

a quantity that has both magnitude and direction

vector

200

If 

c=201,

∠A=80∘

 and 

∠B=46∘

b = ? 

178.719731320079

300

Consider the vector v between (−4.8,4.9) and (−4.7,−4.4)

If the tip of v is at (−4,0.1) then its tail is at...

(−4.1,9.4)

400

Suppose we have a triangle with A=40∘, B=60∘ and c=4. Then a=...?

2.61081457866456

500

Suppose a car is traveling at 55 km/hr, and that the positive y-axis is north and the positive x-axis is east. Resolve the car's velocity vector (in 2-space) into components if the car is traveling in the north west direction ?

v=⟨−55/√2, 55/√2⟩