Inverse Trig, Law of Sines and Cosines, and Identities

Simplify using identities 1

100

sec(theta)cos(theta)

1

200

(sin^2theta + cos^2theta)/csc(theta)

sin(theta)

300

costhetasectheta-(costheta/sectheta)

sin^2theta

400

sec^2theta/(sec^2theta-1)

csc^2theta

500

(1+costheta)(csctheta-cottheta)

sin(theta)

600

(costheta-sintheta)^2 + (costheta + sintheta)^2

2

Identities

100

1/csctheta

sintheta

200

sin^2(theta) + cos^2(theta)

1

300

1-csc^2alpha

-cot^2alpha

400

sin(-theta)

-sintheta

500

(sec^2theta-1)/(1-sec^2theta)

-1

600

(sin^4(theta)-cos^4(theta))/(sin(theta)-cos(theta)

sin(theta)+cos(theta)

Inverse Trig Functions

100

How many solutions exist when 

cos(theta)=-1.5

None!

200

Evaluate 

cos^(-1)(1/2)

60^o

300

Evaluate

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

60^o

400

Solve for  0^o<theta<360^o

5/2=2+sin(theta)

30^o or 150^o

500

Solve for all possible angles theta: 

-1=-1-costheta

90^o +360^o k or 270^o +360^o k

Law of Sines

100

Could you use the law of sines if: side a=5 side b=3 and side c=7?

No, SSS triangles are solved with the law of cosines!

200

How many triangles if: A=52^o c=18 and a=12

No Triangles!

300

How many triangles?  X=58^o side y=30 and side x=26

Two triangles!

400

Solve for angle C if: A=34^o c=34 and a=31

C= 37.8^o   or   C=142.2^o

500

Solve for angle B if: A=21^o  c=16 and a=15

B=1.5^o   or   B=136.5^o

Law of Cosines

100

Find angle A if angle C = 34^o side b=11 and side a =17

A = 108^o

200

Solve for angle A if: a=10, c=17, and b=11

A=34^o

300

How many triangles if: 

C=141^o  b=31 and c=17

None!

400

Solve for angle B if: 

b=22.7, a=6.7, and C=94.8^o

B=69.2^o

Potpourri!

100

What is Mr. Laviolette's dog's name?

Maya

200

What is Mr. Laviolette's favorite color?

Orange

300

What is Mr. Laviolette's favorite number

2 or e

400

What is Mr. Laviolette's favorite branch of math?

Set Theory!