Trig Jeopardy

Unit Circle

100

The full circumference of a unit circle in radians

2*pi

200

Half the circumference of a unit circle in degrees

180

300

The "y-values" of the unit circle

sine

400

2pi - pi/3

5pi/3

500

pi/3 + 3pi/4

13pi/12

Pythagorean Identities

100

the definition of csc(x)

1/sin(x)

200

def of tan(x)

sin(x)/cos(x)

300

1+cot²(x)=

csc(x)

400

tan²(x)+1=

sec²(x)

500

1=

sin²(x)+cos²(x)

Angle Sum and Difference Identities

100

sin(a+b)=

sin(a)cos(b)+cos(a)sin(b)

200

sin(a-b)=

sin(a)cos(b)-cos(a)sin(b)

300

cos(a+b)=

cos(a)cos(b)-sin(a)sin(b)

400

cos(a-b)=

cos(a)cos(b)+sin(a)sin(b)

500

tan(a-b)=

(tan(a)-tan(b))/(1+tan(a)tan(b))

Double and Half Angle Identities

100

sin(2x)=

2sin(x)cos(x)

200

cos(2x)=

cos(2x)–sin(2x) = 1–2sin(2x) = 2cos(2x) – 1

300

tan(2x)=

(2tan(x))/(1-tan²(x))

400

sin(x/2)=

(+/-)sqrt((1-cos(x)/2)

500

cos(x/2)=

(+/-)sqrt((1+cos(x)/2)

Sum and Product Identities

100

sin(x)+sin(y)=

2sin((x+y)/2)cos((x-y)/2)

200

cos(x)+cos(y)=

2cos((x+y)/2)cos((x-y)/2)

300

cos(x)-cos(y)

-2sin((x+y)/2)sin((x-y)/2)

400

sin(x)cos(y)=

(1/2)(sin(x+y)+sin(x−y))

500

cos(x)cos(y)=

(1/2)(cos(x−y)+cos(x+y))