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Trig Verify

100

tan²(x) + 1 = sec²(x)

tan²(x) + 1 = sec²(x)

sec²(x) = sec²(x)

200

2csc(x)sec(x) = csc(2x)

2csc(x)sec(x) = csc(2x)

1/(2sin(x)cos(x)) = csc(2x)

1/(sin(2x)) = csc(2x)

csc(2x) = csc(2x)

300

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

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

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

cos(x) = cos(x)

400

cos(pi) + cos(pi/2) = -1

cos(pi) + cos(pi/2) = -1

2cos(3pi/4)cos(pi/4) = -1

-sqrt(2)((sqrt(2))/2) = -1

-2/2 = -1

-1 = -1

500

tan(2x) = sin(2x)

tan(2x) = sin(2x)

(2tan(x))/(1-tan²(x)) = sin(2x)

(2tan(x))/sec²(x) = sin(2x)

2tan(x)cos²(x) = sin(2x)

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

sin(2x) = sin(2x)

Trig Solving Without Identities

100

sin(2x) = 0

x = 0, pi, 2pi, . . .

x = pi/2, 3pi/2, . . .

200

cos(2x) - cos(4x) = 0

x = 0, pi/3, 2pi/3, . . .

x = 0, pi, 2pi

300

6tan(4x) = 24

x = 0.3325

x = 1.1175

400

sqrt((1-cos(x))/2) = (sqrt(2))/2

x = pi/2, 3pi/2, . . .

500

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

x = 1.57 or pi/2

Misc. Trig

100

Find the exact value of sin(30°) + cos(60°)

sqrt(2)/2 + 1/2

200

sin(x) = sqrt(2)/2 and is in quadrant 1, solve tan(x)

tan(x) = 1

300

Solve for the period of y = 2sin(3x - pi/2)

Period = (2pi)/3

400

Simplify: (cos²x + sin²x)/(2sinxcosx)

cot(2x)

500

See paper for problem

See paper for answer

Watertown Trivia

100

This river makes up most of the southern border of Watertown.

What is the Charles River?

200

This is Watertown's zip code.

What is 02472?

300

Watertown was founded in this year.

What is 1630?

400

This is the area of Watertown to the nearest mi².

What is 4 mi²?

500

According to the 2020 census, this was the population of Watertown to the nearest thousand.

What is 35,000?