FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!

Trigonometry Trivia Quiz

I became a trigonometry teacher for the school year 2006. Here's a quiz on some of the basics of "Trig". (The Greek letter name, pi, is used for the ratio of the circumference of a circle to its diameter.)

A multiple-choice quiz by TonyTheDad. Estimated time: 6 mins.

Author
TonyTheDad

Time
6 mins

Type
Multiple Choice

Quiz #
250,308

Updated
Dec 03 21

# Qns
10

Difficulty
Difficult

Avg Score
5 / 10

Plays
1702

Last 3 plays: Guest 112 (0/10), Guest 100 (5/10), Guest 101 (1/10).

One at a Time - Single Page - Timed Game

Question 1 of 10

1. In trigonometry, angles are formed by the rotation of a ray about its endpoint from an initial position to a terminal position. The measure of an angle can be negative or positive, depending on the direction of its rotation. Which direction of rotation returns negative angles: counter-clockwise (ccw) or clockwise (cw)?

Answer: (Answer ccw or cw only)

NEXT>

Question 2 of 10

2. The two main trigonometric functions, sine (sin) and cosine (cos) differ by the addition of the prefix "co" to "cosine." From where does the "co" derive? Hint

Constant

Coefficient

Complementary

Constraint

NEXT>

Question 3 of 10

3. The functions cotangent, secant, and cosecant have what relationship to the functions tangent, cosine, and sine (respectively)? Hint

reciprocal

inverse

cofunctions

supplementary

NEXT>

Question 4 of 10

4. Angles are measured in degrees or in radians. The conversion factor with which to multiply to convert from degrees to radians is: Hint

pi/180

2pi

180/pi

1/2pi

NEXT>

Question 5 of 10

5. The sine function is an odd function (as opposed to even). Which of these statements holds true for a general odd function, f? Hint

f(x) = f(-x)

f(x) = f(n*x), where n is any odd integer

f(x) = n*f(x), where n is any odd integer

f(-x) = -f(x)

NEXT>

Question 6 of 10

6. The cosine function is an even function (as opposed to odd). Which of these statements holds true for a general even function, f? Hint

f(-x) = -f(x)

f(x) = f(n*x), where n is any even integer

f(x) = n*f(x), where n is any even integer

f(x) = f(-x)

NEXT>

Question 7 of 10

7. There are 8 trigonometric identities called Fundamental Identities. Three of these are called Pythagorean Identities, because they are based on the Pythagorean Theorem. Which of the following is NOT a Pythagorean Identity? Hint

1 + tan^2 x = sec^2 x

sin^2x + cos^2 x = 1

1 + sec^2 x = csc^2 x

1 + cot^2 x = csc^2 x

NEXT>

Question 8 of 10

8. The sum identity for cosine can be summarized as: Hint

cos(A+B) = cos(A)cos(B) + sin(A)sin(B)

cos(A+B) = cos(A)sin(B) + sin(A)cos(B)

cos(A+B) = cos(A)sin(B) - sin(A)cos(B)

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

NEXT>

Question 9 of 10

9. If you know the following data about a triangle and wish to solve the triangle (find all the missing side and/or angle values), which one is ambiguous; i.e., there may be zero, one, or two solutions for the missing values? Hint

Two angles and any side

Three sides

Two sides and an angle opposite one side

Two sides and the included angle

NEXT>

Question 10 of 10

10. Inverses: the relations "arcsin x" and "Arcsin x" differ in spelling because the latter's name is capitalized. What is the distinction of the capitalization? Hint

capitalized indicates relation is graphed in polar coordinates

no difference

capitalized spelling indicates limited range

capitalized indicates return value is in radians

(Optional) Create a Free FunTrivia ID to save the points you are about to earn:

Select a User ID:

Choose a Password:

Your Email:

Most Recent Scores

Oct 29 2024 : Guest 112: 0/10
Oct 24 2024 : Guest 100: 5/10
Oct 01 2024 : Guest 101: 1/10
Sep 25 2024 : Guest 143: 0/10
Sep 24 2024 : Guest 110: 3/10
Sep 15 2024 : Guest 108: 4/10
Sep 02 2024 : Guest 89: 4/10

Score Distribution

Quiz Answer Key and Fun Facts

Answer: cw

This is often confusing to students, as angles in geometry are always positive.

2. The two main trigonometric functions, sine (sin) and cosine (cos) differ by the addition of the prefix "co" to "cosine." From where does the "co" derive?

Answer: Complementary

Sine and cosine are known as cofunctions to each other; i.e., the sin of an angle is the same as the cosine of that angle's complement [sin(A) = cos(90-A) and cos(A) = sin(90-A)].

Other cofunction pairs are tangent/cotangent and secant/cosecant.

3. The functions cotangent, secant, and cosecant have what relationship to the functions tangent, cosine, and sine (respectively)?

Answer: reciprocal

Using reference triangle parameters, cot A = x/y, csc A = r/y, and sec A = r/x. These are reciprocals of the definitions for tangent (tan A = y/x), sine (sin A = y/r), and cosine (cos A = x/r).

This relationship can also be expressed as cot A = 1/tan A, csc A = 1/sin A, and sec A = 1/cos A.

Also, the terms inverse and reciprocal are sometimes used synonymously in other diciplines. Reciprocal is more correctly the multiplicitive inverse. A regular inverse is a relation that interchanges the domain and range of another relation. For example: y=2x+8 and x=2y+8 would be inverses of each other, as their domain and range variables are swapped.

4. Angles are measured in degrees or in radians. The conversion factor with which to multiply to convert from degrees to radians is:

Answer: pi/180

There are 360 degrees (2pi radians) in a full circular rotation. The ratio of radians to degrees is therefore 2pi/360, or pi/180.

5. The sine function is an odd function (as opposed to even). Which of these statements holds true for a general odd function, f?

Answer: f(-x) = -f(x)

Any function having the property that for each x in the domain, -x is also in the domain and f(-x) = -f(x), is called an odd function.

6. The cosine function is an even function (as opposed to odd). Which of these statements holds true for a general even function, f?

Answer: f(x) = f(-x)

Any function having the property that for each x in the domain, -x is in the domain and f(-x) = f(x) is called an even function.

Answer: 1 + sec^2 x = csc^2 x

The Pythagorean Identities can be solved for any of their terms, then used in substitutions for trigonometric proofs.

8. The sum identity for cosine can be summarized as:

Answer: cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

The sum identity for cosine actually subtracts its terms. The difference identity adds its terms.

And remember: The trigonometric functions are *not* distributive; i.e., cos(A+B) does *not* equal cos A + cos B.

Answer: Two sides and an angle opposite one side

If you know three sides, you can use the Law of Cosines to solve for the angles.

If you know two sides and the included angle, again you can use the Law of Cosines to solve for the missing side, then solve for the missing angles.

If you know two angles and any side, you can first use the Interior Angle Theorem to solve for the missing angle. Then, you can use the Law of Sines to solve for the missing two sides.

However, knowing two sides and an angle opposite can have 6 different variations: 2 have no solution, 3 have 1 solution, and 1 has two different solutions.

10. Inverses: the relations "arcsin x" and "Arcsin x" differ in spelling because the latter's name is capitalized. What is the distinction of the capitalization?

Answer: capitalized spelling indicates limited range

By restricting the range of the corresponding inverse relation, it is possible to define an inverse function for all the trigonometric inverses.

Source: Author TonyTheDad

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.