Chapter 5 Trig Review

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 tan a = (1/5) find cot a

What is cot a = (1/tan a )

=(1/(1/5))

=(5/1)

=5

300

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)

400

Simplify:

csc x - cos x cot x

What is csc x-cosx cot x = (1/sinx)-cosx(cosx/sinx)

=(1/sin x)-((cos²x)/(sinx))

=((1-cos²x)/(sinx))

=((sin²x)/(sinx))

=sinx

500

Simplify:

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

Verifying/Simplifying Trig. Identities

100

(sec²x-1)cos²x = sin²x

What is (sec²x-1)cos²x

=(tan²x)cos²x    Pythagorean Identity

=((sin²x)/(cos²x))cos²x  Quotient Identity

=sin²x   Multiply and divide out common factor

200

sec²x(1-cos²x) = tan²x

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

300

sinx-sinx cos²x=sin³x

What is sinx-sinx cos²x

=sinx(1-cos²x)  Factor

=sinxsin²x  Pythagorean Identity

=sin³x Multiply

400

cot²x csc²x-cot²x=cot⁴x

What is cot²xcsc²x-cot²x

=cot²(csc²x-1)  Factor

=cot²xcot²x  Pythagorean Identity

=cot⁴x Multiply and add exponents 

500

tanx csc²x-tanx = cot x

What is tanx csc²x-tanx

=tanx(csc²x-1) Factor

=tanx cot²x Pythagorean Identity

=((sinx)/(cosx))*((cos²x)/(sin²x)) Quotient Identities

=(cosx)/(sinx)  Multiply and divide common

=cot x quotient identity

Trig Equations

100

Find the solutions on the unit circle in degrees:

4=-8cos(x)

(2pi)/3, (4pi)/3 + 2pin

200

Find the solutions on the unit circle in radian:

5=1+2csc(x)

pi/6, (5pi)/6 + 2pin

300

Find the solutions on the unit circle in radians:

-4=-2+2tan(x)

(3pi)/4 + pin

400

Find the solutions on the unit circle in radians:

-csc(x)+cot(x)=-1

pi/2 +2pin

500

Find the solutions on the unit circle in degrees:

0=-2cot(x)-csc²(x)

(3pi)/4 + pin

Solving Trig. Equations

100

5sinx+2=sinx [0,2pi]

What is 5 sinx+2=sinx

=4sinx+2=0

=2(2sinx+1)=0

=2sinx=-1

= sinx=(1/2)  

((7pi)/6) and ((11pi)/6)

. 

200

2-10secx=4-9secx [0, 2pi]

What is 2-10secx=4-9secx

=-10secx=2-9secx

=-secx=2

=secx=-2  = cosx=-(1/2)

((2pi)/3) and ((4pi)/3)

300

5=sec²x+3 [0,2pi]

What is 5=sec²x+3

= 2=sec²x

=(+/-)(√2)=(√sec²x)

= secx=(+/-)(√2)

= cosx=(+/-)(1/(√2))*((√2)/(√2))

= cosx=(+/-)((√2)/2)

=

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

400

3cscx=2cscx+(√2) [0,2pi]

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)

Random - Can only be every 3rd Question

100

In the card game sheepshead, who is a player who passes the opportunity to pick the blind despite having a powerful hand.

Maurer

 The term “mauer”, used as a noun, is loosely translated as “coward”. In German “Mauer” is a stone wall – like a city wall; “der Mauerer” is the stone mason who builds such walls, and is used in card games to describe a very cautious player;

200

This fish, popularized by the the deep sea in Finding Nemo, mate using parasitism.  This is where the male fuses itself together with the female for the rest of their lives. 

Anglerfish

300

The first Micky released in public was not names Micky.  He was seen whistling and holding the helm.  What was his name?

Steamboat Willie

400

The oldest living land animal on earth is a 192-year-old and is named Jonathan.  What kind of animal is this?

Turtle!

500

What is the only part of the body that can't heal itself?

Teeth