Trig-pardy

Trig. Identities

100

If cos x = (2/3) find sec x

What is sec x = (1/cos x)

=(1/(2/3))

=(3/2)

200

if cos x = (1/6) and sin x = ((√35)/6) find cot x

What is cot x = ((cos x)/(sin x))

=((1/6)/(√35)/6)

=(1/(√35)) * ((√35)/(√35))

=((√35)/35)

300

PASS GO

Gain 500 points

400

The exact value of sin(15^o).  Use an identity.

What is (sqrt6 - sqrt2)/4 ?

500

The exact value of cos(75⁰).  Use an identity.

What is (sqrt 6 - sqrt 2)/4 ?

Verifying/Simplifying Trig. Identities

100

sec²x(1-cos²x)

What is sec²x(1-cos²x)

=sec²x-sec²xcos²x   Distributive Property

=sec²x-(1/(cos²x))*cos²x Reciprocal Identity

=sec²x-1 Multiply and divide out common factor

=tan²x Pythagorean Identity

200

cot²x csc²x-cot²x=cot⁴x

What is cot²xcsc²x-cot²x

=cot²(csc²x-1)  Factor

=cot²xcot²x  Pythagorean Identity

=cot⁴x Multiply and add exponents 

300

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.

400

PICK A NUMBER (Between 0-1000)

Lose that many points

500

csc x sec x - tan x

What is csc x sec x - tan x = (1/sinx)*(1/sinx)-(sinx/cosx)

=(1/(sinxcosx))-(sinx/cosx)

=(1/(sinxcosx))-(sinx/sinx)(sinx/cosx)

=((1-sin²x)/(sinxcosx)

=((cos²x)/(sinxcosx)

=(cosx/sinx)

=cotx

Trig Equations

100

Find the solutions on the unit circle in degrees:

4=-8cos(x)

120 and 240

200

Find the solutions on the unit circle in degrees:

5=1+2csc(x)

30 and 150

300

BANKRUPT

Lose all your points

400

All radian solutions [0,2pi) of 2cos²x + cosx - 1 = 0

What are pi/3, 5pi/3, and pi?

500

The exact value of sin(2x) if cosx = 1/4 and x is in quadrant 4.  Use an identity.

What is (- sqrt 15)/8 ?

Solving Trig. Equations

100

5sinx+2=sinx

What is 5 sinx+2=sinx

=4sinx+2=0

=2(2sinx+1)=0

=2sinx=-1

= sinx=(1/2)  The period of sine is (2pi), so you only need to find solutions on the interval [0,(2pi)].  The solutions on this interval are ((7pi)/6) and ((11pi)/6). 

200

PICK A NUMBER (Between 0-1000)

Gain that many points

300

2-10secx=4-9secx

What is 2-10secx=4-9secx

=-10secx=2-9secx

=-secx=2

=secx=-2  = cosx=-(1/2)

((2pi)/3)+2npi, ((4pi)/3)+2npi, neZ

400

3cscx=2cscx+(√2)

What is 3cscx=2cscx+(√2)

= cscx=(√2)

= sinx=(1/(√2))*((√2)/(√2))

= sinx=(√2)/2)

=(pi/4), ((3pi)/4)

500

11=3csc²x+7

What is 11=3csc²x+7

= 4=3csc²x

=(4/3) = csc²x

= (+/-)((√(4/3))=(√csc²x)

=cscx = (+/-)(2/(√3))or(+/-)(2(√3)/3)

= sinx=(+/-)(√3/2)

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

Snapple Facts

100

This island is the largest in the Continental U.S.

What is Long Island? Snapple Fact #333

200

This letter was the last letter to be added to the English alphabet 

What is J?  Snapple Fact #336

300

This aquatic mammal sleeps with one eye open

What is a dolphin? Snapple Fact #760

400

PICK A TEAM

Swap Points with that team

500

This is Barbie's full name

What is Barbara Millicent Roberts?  Snapple Fact #902