Trigonometric Identities and Equations

Inverse Trig

100

What is the domain and range of tan^-1x?

domain= -infinity to infinity

range: -𝛑/2 to 𝛑/2

200

What is the domain and range of inverse cosine

Domain [-1, 1]

Range [0, 𝛑]

300

What is the domain and range of sin^-1x?

domain: [-1, 1]

Range: [-𝛑/2, 𝛑/2]

400

What is the cos (sin^-1(1/2))

√3/2

500

What is the cos^-1(cos(5𝛑/4))?

3𝛑/4

Solving Trig Equations

100

When you find all solutions to a trig equation, what do you need to put at the end of your answers? 

solution +2n𝛑  for n=0, 1, 2, -1, -2 etc.

(sometimes is k𝛑 instead of 2n𝛑)

200

Between 0<x<2𝛑 find solution to 

cscx-sqrt2=0

𝛑/4, 3𝛑/4

300

Solve each equation for exact solution 0<x<2𝛑.

cos 2x=1-3sinx

0,𝛑

400

What is the co-terminal angle of

theta=-310^o

50^o

500

What are all possible solutions for 

sin2-sinx=0

0+2kpi,pi/3+2kpi, pi+2kpi,(5pi)/3+2kpi

Sum and Difference Identities

100

What is 

sin (alpha - beta)

sin alpha cos beta -cos alpha sin beta

200

what is 

cos alpha +beta

cos alpha cos beta-sin alpha sin beta

300

What is the

tan alpha-beta

(tan alpha-tanbeta)/(1+tan alpha tan beta

400

Write in terms of a single trigonometric function

cos100cos65+sin100sin65

cos(100-65) or cos(35)

500

What is 

cos(beta-alpha)

cos beta cos alpha+ sin beta sin alpha

Ms. Allen :p

100

Ms. Allen went to college here 

What is Washburn 

200

Ms. Allen's dog's name is... 

Budder

300

Ms. Allen played all of the following sports expect...

Volleyball 

Softball 

Basketball 

Basketball 

400

Ms. Allen drives this car... 

Chevy Sonic 

500

Ms. Allen's birthday is.. 

September 30th 

Verifying Trig Identities

100

What are the three fundamental identities

sin²x+cos²x=1

1+tan²x=sec²x

1+cot²x=csc²x

200

What are the six ratio identities?

tan=sin/cos

cot=cos/sin

sin=1/csc

cos=1/sec

sec=1/cos

csc=1/sin

300

What are some tips for solving trig identities

Answers include

-work on one side only

-start with more complicated side

-treat each side seperately

-Factoring, adding or subtracting fractions, simplifying complex fractions

-Use basic fundamental identities

-convert to sines and cosines

400

How is the verification of identities different than solving trig equations?

Verification you are working with one side to manipulate it to look like the other side.

Solving equations you are still kind of manipulating but you can work with both sides, and there are specific answers you are looking for. 

500

Is this an identity?

cos^3x+cosxsin^2x=cosx

Yep! (Explain how you got that answer?)