Trig Identities
Trig Applications
Vectors
Polar Equations
Sequences & Series
100

Simplify: sin2θ+cos2θ

1

100

Find the amplitude of y=3sinx

3

100

Find the magnitude of <3,4>

5

100

Convert r=4cosθ to rectangular form

(x-2)2+y2=4

100

Find the 7th term: 2,5,8,11...

20

200

Verify the identity: tanx/secx=sinx

since tanx=sinx/cosx and secx=1/cosx, sinx=sinx

200

Find the period of y=cos2x

pi

200

Find the magnitude of the sum of the two vectors <2,-1> and <5,3>

root53

200

Explain what r=3 looks like on a graph.

A circle centered at the origin with a radius of 3.

200

Find the common ratio: 16,24,36,54...

3/2

300

simplify completely: sec2x-1/tanx

tanx

300

Identify the phase shift: y=2sin(x−pi/3)

right pi/3

300

Find the dot product: <1,2> * <3,4>

11

300

Find the point when r=2 and θ=pi/2

(0,2)

300

Find the sum of the 1st 6 terms (starting at k=1) of the sequence 2k+1.

48

400

Solve on 0≤x<2pi: 2cos2x−3cosx+1=0

x=0,pi/3,5pi/3

400

A Ferris wheel with radius 25 ft rotates once every 40 seconds. The center is 30 ft above the ground. Write a sinusoidal model for the rider’s height if the rider starts at the lowest point.

h(t)=30-25cos((pi/20)t)

400

Find a unit vector in the direction of <6,8>

<3/5, 4/5>

400

Determine the symmetry of r2=4sin2θ

Symmetric about the pole.

400

Determine whether the series converges or diverges. If it converges find the sum. 6-1/6+1/216-1/7776+...

Converges. S=216/37

500

Verify the identity: 1−sin⁡x/cos⁡x=cos⁡x/1+sin⁡x

cross multiply and you get cos2x=1-sin2x which is an identity

500

The height of a rider on a Ferris wheel is modeled by: h(t)=18+15sin⁡(pi/6(t−3)). Find the first time the rider reaches a height of 18 after t=0

t=3

500

The two vectors <2,5> and <x,4> are perpendicular. Find x

-10

500

A curve is given by: r=4sin⁡θ. A point P lies on the curve such that the tangent line at P is horizontal. What is the Y-value of P

4

500

The sum of the first n odd positive integers is 12,769. Find n.

n=113

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