Unit 4A PreCal

Identities

100

What is the sine and cosine pythagorean identity? 

sin^2(x)+cos^2(x)=1

200

What is the reciprocal identities of sin(theta)? 

1/cosec(theta)

300

What is two ways to write tanx?

1/cotx  and sinx/cosx

400

What is the Pythagorean identity that has tanx?

1+tan^2(x)=sec^2(x)

or

tan^2(x)=sec^2(x)-1

500

Write all three pythagorean identities that has cot^2(x)

1+cot^2(x)=cosec^2(x)

cot^2(x)=cosec^2(x)-1

cosec^2(x)-cot^2(x)=1

Converting Angles

100

convert pi/6 to degrees 

30^o

200

convert -90^o to radians

-pi/2

300

convert pi/4 to degrees

45⁰

400

convert 2pi/3 to degrees 

120^o

500

convert 500^o to radians

25pi/9

or 

7pi/9

Simplify Trig Expressions

100

sinx*cotx

cosx

200

secx/cscx

tanx

300

tanx/secx

sinx

400

sin(t)-sin(t)cos^2(t)

sin^3(t)

500

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

cosx

Trig values

100

sin(45^o)

sqrt(2)/2

200

cos(pi/3)

1/2

300

tan(pi/4)

1

400

sec(pi/6)

2/sqrt(3)

or 

2sqrt3/3

500

sin(3pi/2)

-1

Trig equations 0<x<2pi

100

Solve the following

2+sinx=2

0, pi

200

Solve the following

-8cosx=-4sqrt(3)

pi/6, 11pi/6

300

Solve the following

-3tanx=0

0, pi

400

Solve the following

2cos(2x)=-1

pi/3, 2pi/3, 4pi/3, 5pi/3

500

Solve the following

2sin^2(x)-3sinx+1=0

pi/6, pi/2, 5pi/6