Trigonometry

Verifying Trig Identities

Solving Trig Identities

Misc. Trig

Watertown Trivia

100

Verify:
cot²x = csc²x - cosxsecx

cot²x = csc²x - cosxsecx
cot²x = csc²x - 1
cot²x = cot²x

100

Solve the following with x = π (pi):

sin(x)tan(x) = a

What is a = 0?

100

This value is the tangent of -210°

What is -√(3)/2?

100

This animal is the mascot of Watertown Middle School.

What is an eagle?

200

Verify:
cot²x - csc²x = 1 - 2(1-cos²x) - 2cos²x

cot²x - csc²x = 1 - 2(1-cos²x) - 2cos²x
cot²x - csc²x = 1 - 2sin²x - 2cos²x
cot²x - csc²x = cos2x - 2cos²x
cot²x - csc²x = -1
cot²x - csc²x = cot²x - csc²x

200

Express a in terms of tan(x/2)

a = sin(x) / 1 + cos(x)

a = tan(x/2)

200

This angle is the angle of elevation from a point 50 m away from the base of a building to 10 m above that building, if the angle of elevation to the top is 60 degrees

What is 62.63 degrees?

200

This was Watertown's population in 2023 (nearest thousand).

What is 35,000?

300

Verify:

cos2x = 1/(1-sin²x) - cot²x - 2(1-cos²x)

cos2x = 1/(1-sin²x) - cot²x - 2(1-cos²x)
cos2x = 1/(cos²x) - cot²x - 2(1-cos²x)
cos2x = csc²x - cot²x - 2(1-cos²x)
cos2x = 1 - 2(1-cos²x)
cos2x = 1 - 2sin²x
cos2x = cos2x

300

Solve the following for x:

sin²x - 2sin²x + cos²x = -1

x = π / 2

300

This bearing is the bearing at which a ship must aim for if it wants to return to an island it left going 200 m N30(degrees)W and then 100 m E50(degrees)S

What is 49.28 m?

300

In this year, Watertown was founded.

What was 1630?

400

Verify:

sin(2+2x) = sin2cos²x - sin2sin²x + 2cos2sinxcosx

sin(2+2x) = sin2cos²x - sin2sin²x + 2cos2sinxcosx
sin(2+2x) = sin2(cos²x-sin²x) + cos2(2sinxcosx)
sin(2+2x) = sin2(cos²x-sin²x) + cos2sin2x sin(2+2x) = sin2cos2x + cos2sin2x
sin(2+2x) = sin(2+2x)

400

Given that

tan⁡(x)+cot⁡(x)=4,

find the exact value of...

tan⁡²(x)+cot⁡²(x)

(tanx + cotx)²

4² = tan²x + cot²x + 2

14 = tan²x + cot²x

Answer = 14

400

This measure is the angle ABC of a triangle by the same name, in which side AB has length sin^-1(21028912/42057824) in Q1 (degrees), side BC has length cos^-1(0.5*3/sqrt(3)) in Q1 (degrees), and side CA has length 18

What is 34.92 degrees?

400

This army rank was the one held by Richard Moxley.

What is private first-class?

500

Verify:
tan(2x) = 2tanx / ( (1-2sin²x)/(cos2x +sin²x) )

tan(2x) = 2tanx / ( (1-2sin²x)/(cos2x +sin²x) )
tan(2x) = 2tanx / ( (1-2sin²x)/(cos²x) )
tan(2x) = 2tanx / ( (1-2sin²x)/(cos²x) )
tan(2x) = 2tanx / ( (cos²x - sin²x)/(cos²x) )
tan(2x) = 2tanx / ( cos²x/cos²x - sin²x/cos²x )
tan(2x) = 2tanx / (1 - tan²x)
tan(2x) = tan(2x)

500

Solve four values of x:

sin(x)cos(x) - 0.5sin(x) = 0

sin(x) (cos(x) - 0.5) = 0

sin(x) = 0, pi

cos(x) = pi/3, 5pi/3

Answers: 0, pi, pi/3, 5pi/3

500

This is the area of a triangle with side lengths 1, 2, and 3!

What is 7.685 units squared?

500

This phrase is Watertown's motto.

What is "in pace condita"?