Week 4

Graphing

100

What are the transformations for this function? y=tan(x+pi/4)-1

down 1, left pi/4

200

What are the transformations on this graph? g(x)=3tan(x+pi/3)-2

down 2, left pi/3, stretched by 3  

300

y=-2tan(x/2)

Graph 1

400

f(x)=3tan(x-pi/2)-1

Graph 2

500

f(x)=-1/2 tan(x+3pi/4)

Graph 3

Trig Identities

100

What are the three Pythagoren Identities?

cos²x+sin²x=1

1+tan²x=sec²x

cot²x+1=csc²x

200

What is sin(-x)

-sin(x)

300

cos(-x)=?

cos(x)

400

tan(-x)=?

-tan(x)

500

What is cos(pi/2 - x)=?

sin(x)

Double Angles

100

sin(2x)

2sin(x)*cos(x)

200

tan(2x)

2tan(x) / (1-tan²x)

300

Find sin(2x) of a right triangle with sides 5, 12, and hypotenuse 13. 

2sin(x)cos(x)

2(5/13)(12/13)

= 120/169

400

Find the exact value of the expression using double angles

sin(120 degrees)

sin(2x)=2sin(x)cos(x)

sin(120) = sin(2*60)

= 2sin(60)cos(60)

=2(1/2)(rad(3)/2)

sin(120)=rad3/2

500

cos(2x)=?

cos²(x)-sin²(x)

2cos²(x)-1

1-2sin²(x)

Half Angles

100

cos(x/2)

rad( 1+cos(x) / 2)

200

sin(x/2)

rad (1-cos(x)/2)

300

If cosx=24/25 and 3pi/2 < x < 2pi

Find sin(x/2)

rad(2) / 10 

400

Use the half angle identity to find the exact value

sin(5pi/6)

sin(x/2) = rad((1-cosx)/2)

x/2 = 5pi/6 -> x=10pi/6 = 5pi/3

sin(5pi/6)=sin(5pi/3 * 1/2)

= rad( (1-cos(5pi/3)) / 2)

= rad((1-1/2) / 2)

= rad (1/2 * 1/2) = rad (1/4) = 1/2 

500

tan(x/2)

rad ( (1-cos(x)) / (1+cos(x)) )

sin(x) / 1+cos(x)

1-cos(x) / sin(x)

Marvel Trivia

100

What was the first Marvel movie made?

What is Iron Man?

200

Who is Black Panther's little sister?

Who is Shuri?

300

What is the name of Thor's hammer?

What is Mjolnir?

400

What is the name of the character Hawkeye becomes after Avengers: Infinity War?

Who is Ronin?

500

Which eye does Nick Fury wear a patch over?

What is the left eye?