Equations with Pythagorean Identities

What's the Identity?

100

cos²x+sin²x

1

200

cosx/sinx

cotx

300

sec²x-1

tan²x

400

sin²x-1

-cos²x

500

cot²x-csc²x

-1

Find it on the Unit Circle

100

tanx=1

pi/4 and (5pi)/4

200

sinx=0

0 and pi

300

cosx=-sqrt2/2

(3pi)/4 and (5pi)/4

400

tanx=-sqrt3

(2pi)/3 and (5pi)/3

500

secx=-sqrt2

(3pi)/4 and (7pi)/4

Solve it by Writing as One Trig Function

100

tan^2 x=1-secx

0, pi/3, (5pi)/3

200

2cos^2 x-sinx-1=0

pi/6, (5pi)/6, (3pi)/2

300

2-2cos^2 x=sinx + 1

pi/2, (7pi)/6, (11pi)/6

400

2sin^2 x+3cosx-3=0

0, pi/3, (5pi)/3

500

3sec^2 x-2tan^2 x=4

pi/4, (3pi)/4, (5pi)/4, (7pi)/4

Solve it by Squaring Both Sides

100

sinx=1-cosx

0, pi/2

200

cscx-cotx=1

pi/2

300

sqrt2cotx=cscx

pi/4, (3pi)/4, (5pi)/4, (7pi)/4

400

cosx-2sinx=-1-3sinx

pi. (3pi)/2

500

tanx=3tanx+sqrt3secx

pi/3, (2pi)/3, (4pi)/3, (5pi)/3

Who Said It?

100

"I am the greatest, I said that even before I knew I was."

Mohammed Ali

200

“Life’s not about how hard of a hit you can give … it’s about how many you can take, and still keep moving forward. That’s how winning is done.”

Rocky

300

"Never let the fear of striking out get in your way"

Babe Ruth

400

"Do you believe in miracles? Yes!"

Al Michaels

500

"Excellence is not a singular act but a habit. You are what you do repeatedly."

Shaquille O'Neal