Show:
Unit Circle
Trig functions
sin and cos
Sum and Diff
Legal Moves
100

In what quadrant is the angle  (5pi)/4 

Quadrant III

100

What is tanpi/2?

Undefined

100

 y=-sin((2pix)/3)  What is the amplitude, period, horizontal and vertical shift

Amplitude is 1, period is 3, horizontal and vertical shifts are 0

100

Find the exact value of the expression 

cos(pi/4+pi/3)

1/4(sqrt(2)-sqrt(6))

100

 tanx sec^2x = tanx tan^2x + 1 

Is this a legal move?  Explain.

No.  

tanx sec^2x = tanx (tan^2x + 1)

200

What is the positive and negative coterminal angle of  (4pi)/3 

(10pi)/3 and -(2pi)/3

200

What is  tan^-1(-1) 

-pi/4

200

Where is the domain and range of the graph 

y=2+5cos(6pix)

domain is all real numbers

range is  -3 <= y <= 7 

200

Find the exact AND simplest value of the expression 

sin 100° cos 40° − cos 100° sin 40°

sqrt(3)/2

200

2cos^2x + cosx = 1 

cosx(2cosx+1)=1

cosx = 1;  2cosx+1=1

Are the moves above correct?  Explain.

No, you can only set each factored term equal to 0 if they multiply to be 0

2cos^2x + cosx = 1 

2cos^2x + cosx - 1 = 0

(2cosx-1)(cosx+1)=0

2cosx-1=0;  cosx+1=0

300

Convert  (5pi)/6 to degrees

150 degrees

300

What is csc (5pi)/3 ?

-(2sqrt(3))/3

300

y=2/3cos(x/2-pi/4)

What is the period?  What is the horizontal shift?

period =   4pi  

Horizontal shift =  pi/2 to the right

300

Rationalize  4/(2-sqrt(3) 

8+4sqrt(3)

300

(sinx+1)/(sinx-1)=(sinx+1)/(sinx-1)*(sinx+1)/(sinx+1) = (sin^2x+1)/-cos^2

How was that math? Pretty good? Explain.

No.  

(sinx+1)*(sinx+1) = sin^2x+2sinx+1

400

Determine the quadrant in which  theta lie when csc<0 and tan>0

Quadrant III

400

What is arccos(sin((11pi)/6)) 

(2pi)/3

400

A ferris wheel is 30 meters tall, the center of axle is 20 meters off the ground and rotates every 20 minutes.  What is the highest point that is reached by a passenger riding on the ferris wheel?  What is the lowest point?

Highest point is 35 meters.  Lowest point is 5 meters.

400

Rewrite the expression as the tangent of an single angle

(2tan(100))/(1-tan^2(100))

tan(200)

400

2sinxcosx=sinx 

(2sinxcosx)/sinx = sinx/sinx

2cosx = 1

cosx = 1/2

What's wrong with the moves above?  

2sinxcosx=sinx 

2sinxcosx - sinx = 0

sinx(2cosx-1)=-

sinx= 0;  2cosx-1=0

By dividing sin on both side, we lost the solution sinx=0