Trigonometric Ratios Quiz: Math Trivia Test!

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Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.

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Quizzes Created: 4 | Total Attempts: 25,434

| Attempts: 22,636 | Questions: 18

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Question 1 / 18

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Which side is opposite angle D?

The side opposite angle D is EF.

Explanation

The side opposite angle D is EF.

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About This Quiz

Trigonometric Ratios Quiz: Math Trivia Test! - Quiz

Embark on a mathematical adventure with our "Trigonometric Ratios Quiz"! Designed for students and enthusiasts alike, this quiz challenges your understanding of the fundamental concepts of trigonometry. Trigonometric... see moreratios — sine, cosine, and tangent — are essential tools in mathematics that relate the angles of a triangle to its side lengths. This quiz will test your ability to apply these ratios to solve problems involving right triangles, as well as your understanding of how they function within the unit circle.
Whether you are a high school student looking to reinforce your classroom learning or someone who enjoys brushing up on mathematical principles, this quiz offers a variety of questions to deepen your comprehension and application skills. From basic identification of trigonometric ratios in different quadrants to more complex applications in real-world scenarios, each question aims to enhance your mathematical prowess and precision.
Ready to test your skills? Dive into our Trigonometric Ratios Quiz and discover just how well you can navigate the fascinating world of trigonometry. Perfect for anyone looking to polish their math skills or prepare for upcoming exams! see less

Which side is opposite angle A?

The side opposite angle A is BC.

Explanation

The side opposite angle A is BC.

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Find sin(A).

7/25

24/7

24/25

To find sin(A), we need to use the trigonometric ratio of sine. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, since we only have the fraction 24/25 as the answer, we can assume that A is an acute angle in a right triangle. Therefore, the side opposite A would have a length of 24 and the hypotenuse would have a length of 25. Dividing the length of the opposite side by the length of the hypotenuse, we get 24/25 as the sine of angle A.

Explanation

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Find sin(60).

Sqrt(3)/2

1/2

Sqrt(3)

The sine of 60 degrees is equal to the square root of 3 divided by 2.

Explanation

The sine of 60 degrees is equal to the square root of 3 divided by 2.

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5. Sin(30) = cos(60)

True

False

The given statement is true because the sine of 30 degrees is equal to the cosine of 60 degrees. In a right-angled triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, while the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. In a 30-60-90 triangle, the side opposite the 30 degree angle is equal to half the length of the hypotenuse, and the side adjacent to the 60 degree angle is equal to half the length of the hypotenuse. Therefore, sin(30) = cos(60).

Explanation

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Find sin(D).

12/13

5/13

12/5

The correct answer is 12/13. This can be determined by using the definition of sine in a right triangle. Since sine is equal to the opposite side divided by the hypotenuse, we can see that in this case, the opposite side is 12 and the hypotenuse is 13. Therefore, sin(D) = 12/13.

Explanation

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Find tan(45).

Sqrt(2)

1/sqrt(2)

The tangent of 45 degrees is equal to 1. This can be derived from the fact that the tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In a 45-45-90 right triangle, the opposite and adjacent sides are equal in length, so the tangent is equal to 1.

Explanation

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Find tan(E).

12/5

12/13

5/12

The correct answer is 5/12. This means that the tangent of angle E is equal to 5/12.

Explanation

The correct answer is 5/12. This means that the tangent of angle E is equal to 5/12.

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9. You need a calculator to find tan(45).

True

False

The value of tan(45) can be found without a calculator because it is one of the special angles in trigonometry. The exact value of tan(45) is 1. This is because in a right triangle with a 45-degree angle, the opposite side and adjacent side are equal, making the tangent ratio equal to 1.

Explanation

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10.

Find tan(30).

Sqrt(3)/2

1/2

1/sqrt(3)

The value of tan(30) can be found using the special right triangle with angles 30-60-90. In this triangle, the side opposite the 30-degree angle is 1, the side opposite the 60-degree angle is sqrt(3), and the hypotenuse is 2. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, tan(30) = 1/sqrt(3), as the side opposite the 30-degree angle is 1 and the side adjacent to the angle is sqrt(3).

Explanation

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11. You need a calculator to find cos(60).

True

False

The statement is false because you do not need a calculator to find the value of cos(60). The value of cos(60) is a well-known value in trigonometry, which is equal to 0.5. Therefore, you can easily determine the value without the need for a calculator.

Explanation

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12.

Find cos(45).

Sqrt(2)

1/sqrt(2)

The correct answer is 1/sqrt(2) because the cosine of 45 degrees is equal to the adjacent side divided by the hypotenuse in a right triangle. In a triangle with a 45-degree angle, the adjacent side and the hypotenuse are equal in length. By using the Pythagorean theorem, we can find that the length of both sides is sqrt(2). Therefore, the cosine of 45 degrees is 1/sqrt(2).

Explanation

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13.

Find cos(60).

Sqrt(3)/2

1/2

Sqrt(3)

The cosine of 60 degrees is equal to 1/2. This can be determined using the unit circle or by using the cosine function. In the unit circle, at 60 degrees, the x-coordinate of the point on the unit circle is 1/2. Therefore, the cosine of 60 degrees is 1/2.

Explanation

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14.

Which LEG is adjacent to angle B?

Angle B is formed by the intersection of sides BC and AB. Therefore, the leg adjacent to angle B is BC.

Explanation

Angle B is formed by the intersection of sides BC and AB. Therefore, the leg adjacent to angle B is BC.

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15.

Find cos(B).

24/25

7/25

24/7

Explanation

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16. Sin(45) = cos(45)

True

False

The statement is true because the sine of 45 degrees is equal to the cosine of 45 degrees. This is because the sine function and the cosine function are equal for complementary angles. In a right triangle, the sine of an angle is equal to the cosine of its complement, and vice versa. Since 45 degrees and its complement 45 degrees are equal, their sine and cosine values are also equal.

Explanation

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17. Sin(30) = cos(30)

True

False

The statement sin(30) = cos(30) is false. In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, while the cosine of an angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. In a 30-60-90 triangle, the sine of 30 degrees is 1/2, while the cosine of 30 degrees is √3/2. Therefore, sin(30) is not equal to cos(30).

Explanation

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18.