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Misc. Trig

100

Verify the following:

(tanx+cotx)/(cscxsecx)=1

What is...

(sinx/cscx+cosx/sinx)/1/sinxcosx

=(sin²x+cos²x)/cosxsinx/1/cosxsinx

=(sin²x+cos²x)/1

=1?

200

Solve the equation:

cosxsinxtanxcotxsecxcscx=?

What is...

cosx*sinx*sinx/cosx*cosx/sinx*1/cosx*1/sinx

= 1*1

= 1?

300

Solve the equation:

(sinxcosx+cosx*√(1-cos²x))/cotx=?

What is...

cosx(sinx+sinx)/cosx/sinx

= 2sinx/sinx

=2?

400

Can you verify the equation? If so verify!

sin(8x)=8sinxcosx(cos²x-8sin²xcos⁴x-sin²x+8sin⁴xcos²x)

What is....

sin(8x)=2sin4xcos4x

=2(2sin2xcos2x)(cos²2x-sin²2x)

= 2(2(2sinxcosx)(cos²x-sin²x)(1-sin²2x)

= 8sinxcosx(cos²x-sin²x)(1-2sin²2x)

= (8sinxcos³x-8sin³xcosx)(1-2(2sinxcosx)(2sinxcosx)

= (8sinxcos³x-8sin³xcosx)(1-8sin²xcos²x)

= 8sinxcos³x-64sin³xcos⁵x-8sin³xcosx+64sin⁵xcos³x

= 8sinxcosx(cos²x-8sin²xcos⁴x-sin²x+8sin⁴xcos²x)?

500

Can you verify the equation? If so verify!

tan²xcotx/secx=(cos²x+sin²x)/cotx

What is...

CANNOT VERIFY!?

Trig verify-simplify

100

(sin²x+cos²x)/(1+tan²x)=1-sin²x

What is...

(sin²x+cos²x)/(1+tan²x)

= 1/sec²x

= cos²x

=1-sin²x?

200

cscx-sinx=cos²x/sinx

What is...

cscx-sinx

= 1/sinx-sin²x/sinx

= (1-sin²x)/sinx

= cos²x/sinx?

300

(1-tanx)/(1+tanx)+(1+tanx)/(1-tanx)=2secx/(cosx-sinx)

What is...

(1-tanx)/(1+tanx)+(1+tanx)/(1-tanx)

= ((1-2tanx+tan²x)+(1+2tanx+tan²x))/(1+tanx)(1-tanx)

= (2+2tan²x)/(1-tan²x)

= 2(1+tan²x)/(1-tan²x)

= 2sec²x/(cosx-sinx)/cosx

= 2/cos²x/(cosx-sinx)/cosx

= 2/cosx/(cosx-sinx)

= 2secx/(cosx-sinx)?

400

(1-cos²x)/(1-sin²x)*(csc²x-1)=1

What is...

(1-cos²x)/(1-sin²x)*(csc²x-1)

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

= sin²x/cos²x*cot²x

= tan²x*1/tan²x

=1

500

(cos x + cos 3x)/(sin x + sin 3x) = csc 2x - tan x

What is...

(cos x + cos 3x)/(sin x + sin 3x)

= (2 cos(2x)cos(-x))/(2sin(2x)cos(-x))

= (2 cos 2x)/(2 sin 2x)

= (1-2sin²x)/(2sinxcosx)

= 1/(2sinxcosx) - (2sin²x)/(2sinxcosx)

= 1/sin2x - sinx/cosx

= csc 2x - tan x

Trig Solving

100

5 tan x + 3 = 0

5 tan x + 3 = 0

tan x = -3/5

x = -0.540

200

4 sec²x = 0

4 sec²x = 0

4(tan²x + 1) = 0

tan²x = -1

tan x = √-1

UNDEFINED! no solutions

300

sin 5x + sin 9x = 2

sin 5x + sin 9x = 2

2sin(7x)cos(7x) = 2

sin(7x) = 1      cos(7x) = 2

x = 0.224      x = no real solutions

400

1/2(cos(4x-7x)-cos(4x+7x)) = 1

1/2(cos(4x-7x)-cos(4x+7x)) = 1

cos (-3x) - cos(11x) = 0.5

-2sin(4x)sin(-7x)

-2sin(4x) = 0.5       sin (-7x) = 0.5

x = 0.063                 x=0.036

500

sin (3x/2) = 3

sin (3x/2) = 3

√((1-cos 3x)/2) = 3

(1 - cos 3x)/2 = 9

1-cos 3x = 18

-cos 3x = 17

x = no real solutions

Watertown Trivia!

100

The Watertown Middle School principal

Who is Joel Giacobozzi?

200

The 2025 Watertown High School musical

What is Anything Goes?

300

How many schools does Watertown have? Name them!

What is 6?

- Early Steps Preschool

- Cunniff Elementary School

- Hosmer Elementary School

- J.R. Lowell Elementary School

- Watertown Middle School

- Watertown High School

400

How many athletic teams does Watertown High School have?

What is 26?

500

How much is "the-state-of-the-art" new Watertown High School?

What is $220 million?