AP Precalculus (Fall)

Unit Circle

100

cos((5pi)/3)

1/2

200

tan((-7pi)/6)

  -1/\sqrt(3) or 

-\sqrt3/3

300

cot((17pi)/4)

1

400

sin((271pi)/6)

-1/2

500

sec((968433pi)/4)

\sqrt(2)

Inverses

100

cos^(-1)((-\sqrt(2))/2)

(3pi)/4

200

tan^(-1)(-\sqrt(3))

-pi/3

300

 sin^(-1)(-sqrt(3)/2) 

-(pi)/3

400

cos(cos^(-1)(pi))

Does not exist!

500

 sin^(-1)(-1/2)+tan^(-1)(1) 

pi/12

Identities

100

(1-cos^(2)(x))/(sin(x)

sin(x)

200

cot(x)sec(x)

csc(x)

300

(cot(x)+csc(x))^(2)(1-cos(x))-1

cos(x)

400

cos(x)(1+(sec^(2)(x))/csc^(2)(x))

sec(x)

500

sin(x)/(1-cot(x))-cos(x)/(tan(x)-1)-cos(x)

sin(x)

Complex Numbers

100

The number  4[cos((5pi)/6)+isin((5pi)/6)] in rectangular form.

-2\sqrt(3)+2i

200

The number 

 1/2-\sqrt3/2i in polar/trigonometric form

cos((5pi)/3)+isin((5pi)/3)

300

Find the product of  z*w

 z=5[cos(pi/7)+isin(pi/7)] 

 w=2[(cos(pi/3)+isin(pi/3)] 

10[cos((10pi)/21)+isin((10pi)/21)]

400

Find the trigonometric form of the quotient.

 (12[cos((3pi)/5)+isin((3pi)/5)])/(3[cos(pi/10)+isin(pi/10)]) 

4[cos(pi/2)+isin(pi/2)]

500

Write in rectangular form.

 (4[cos(pi/6)+isin(pi/6)])^(3) 

64i

Polar Coordinates

100

Convert the polar coordinates to rectangular.

 (-6,(5pi)/6) 

(3\sqrt3,-3)

200

Convert the rectangular coordinates to polar.

 (-2\sqrt3,-2) 

 (4, (7pi)/6) or

(4, -(5pi)/6)

300

Convert the polar equation to rectangular.

 r=6sin\theta  

 x^2+y^2-6y=0 

OR

x^2+(y-3)^2=9

400

Convert the rectangular equation to polar.

y=4

r=2/cos\theta=2sectheta

500

Convert the polar equation into rectangular.

 r=tanxsecx 

y=x^2