Trig Identities

Trig Verify-simplify

100

4sin(x+y)=4sinxcosy-4cosxsiny

4sin(x+y)=

4(sinxcosy-cosysinx)=

4sinxcosy-4cosysinx

200

(sin²θ-1)-(cos²θ-1)=cos(2θ)  

(sin²θ-1)-(cos²θ-1)=

(cos²θ)-(sin²θ)=

cos(2θ)

300

1-(2(1/cot²x+1)=cos(2x)

1-(2(1/cot²x+1)=

1-(2(1/cscx²x)=

1-(2sin²x)=

cos(2x)

400

tan(x-y)=tanx/1-tanxtany + tany/1-tanxtany

tan(x-y)=

tanx+tany/1-tanx+tany=

tanx/1-tanxtany + tany/1-tanxtany=

500

-2tanθ/sec²θ=2tan/-1-tan²θ

-2tanθ/sec²θ

(-tanθ/sec2θ)+(-tanθ/sec2θ)=

(-tan/1+tan2θ) + (-tan/1+tan2θ)=

(-1/-1)*((tanθ/-1-tan2θ)+(tanθ/-1-tan2θ)*(-1/-1)=

(tanθ/-1-tan2θ)+(tanθ/-1-tan2θ)=

2tan/-1-tan2θ=

Trig solving w-w/0 identities

100

sinθ =1/2

θ = pi/6, 5pi/6

200

1 - 2 sin2 θ =0

sin² θ = 1/2

sinθ = √2/2

θ = pi/2 ..  or θ= 5pi/4

300

sinθ=cosθ

tanθ= 1

θ =pi/4, 5pi/4 ..

400

2sin²θ - sinθ -1 =0

(2sinθ+1)(sinθ-1)=0

sinθ =-1/2  or sinθ =1

θ =-pi/6    0r  θ =pi/2

500

(sin2θ)-(cosθ)=0

2sinθcosθ-cosθ=0

cosθ(2sinθ -1)=0

cosθ=0  or 2sinθ-1=0

θ=pi/2 ...   or θ= pi/6...

Misc. Trig

100

How many answers does x have in:

cosx = 1

infinity: 0, 2pi, 4pi...

200

verify:

(-tan²x-1)/sec²x   =   -1

-1(tan²+1)/sec²

-sec²/sec²

=-1

300

Verify

(cos²x+sin²x)/(1-csc²x)    =         -tan²x

(cos²x+sin²x)/(1-csc²x) 

1/-cot²x

1/-cos²/sin²

-sin²x/cos²x

= -tan²x

400

Verify:

2cos(3pi)sin(pi) = 0

2cos(3pi)sin(pi)

(sin2pi - sinpi)

0-0

=0

500

verify:

sin4xcos2x - cos4xsin2x  =  (2-sec²x)/sec²x

sin4xcos2x - cos4xsin2x  =  (2-sec²x)/sec²x

sin4xcos2x - cos4xsin2x

sin(4x-2x)

sin2x

2cos²x-1

2/sec²x   -  sec²x/sec²x

= (2-sec²x)/sec²

Watertown Trivia

100

Where is the Halfway Cafe Located, __(N,S,E,W) side of watertown

West side of Watertown

200

What is the name of the taco place in front of WHS

Plazita Mexico Tacos

300

How many years has Mr, Spillane been teaching at WHS

21 Yrs

400

What math classes does Ms Zeikel teach

Algebra 2, Geometry, Stats

500

When was the last time the WHS boys soccer team won the Middlesex League Championship

Oct 18 2019