Simplify: sin2θ+cos2θ
1
Find the amplitude of y=3sinx
3
Find the magnitude of <3,4>
5
Convert r=4cosθ to rectangular form
(x-2)2+y2=4
Find the 7th term: 2,5,8,11...
20
Verify the identity: tanx/secx=sinx
since tanx=sinx/cosx and secx=1/cosx, sinx=sinx
Find the period of y=cos2x
pi
Find the magnitude of the sum of the two vectors <2,-1> and <5,3>
root53
Explain what r=3 looks like on a graph.
A circle centered at the origin with a radius of 3.
Find the common ratio: 16,24,36,54...
3/2
simplify completely: sec2x-1/tanx
tanx
Identify the phase shift: y=2sin(x−pi/3)
right pi/3
Find the dot product: <1,2> * <3,4>
11
Find the point when r=2 and θ=pi/2
(0,2)
Find the sum of the 1st 6 terms (starting at k=1) of the sequence 2k+1.
48
Solve on 0≤x<2pi: 2cos2x−3cosx+1=0
x=0,pi/3,5pi/3
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)
Find a unit vector in the direction of <6,8>
<3/5, 4/5>
Determine the symmetry of r2=4sin2θ
Symmetric about the pole.
Determine whether the series converges or diverges. If it converges find the sum. 6-1/6+1/216-1/7776+...
Converges. S=216/37
Verify the identity: 1−sinx/cosx=cosx/1+sinx
cross multiply and you get cos2x=1-sin2x which is an identity
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
The two vectors <2,5> and <x,4> are perpendicular. Find x
-10
A curve is given by: r=4sinθ. A point P lies on the curve such that the tangent line at P is horizontal. What is the Y-value of P
4
The sum of the first n odd positive integers is 12,769. Find n.
n=113