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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
1707

Last 3 plays: Guest 49 (7/10), Guest 158 (1/10), Guest 73 (7/10).

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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)

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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

Coefficient

Complementary

Constraint

Constant

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Question 3 of 10

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

supplementary

cofunctions

reciprocal

inverse

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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

180/pi

pi/180

2pi

1/2pi

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

f(x) = f(-x)

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

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

f(-x) = -f(x)

f(x) = f(-x)

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

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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

sin^2x + cos^2 x = 1

1 + tan^2 x = sec^2 x

1 + cot^2 x = csc^2 x

1 + sec^2 x = csc^2 x

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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)

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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 sides and an angle opposite one side

Two sides and the included angle

Three sides

Two angles and any side

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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

no difference

capitalized spelling indicates limited range

capitalized indicates return value is in radians

capitalized indicates relation is graphed in polar coordinates

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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.
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