The Trigonometry Basics Quiz
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The Trigonometry Basics Quiz

Test your knowledge on the basics of Trigonometry with this quiz! Explore the concepts of angles, distances, and right-angled triangles commonly used in science, engineering, and video games.

Created by
@OrganizedMoldavite

Questions and Answers

Which trigonometric functions are abbreviated as sin, cos, and tan?

Sine, Cosine, and Tangent

What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?

Sine

Which angle is often labeled as θ in trigonometry?

The angle of interest

What is the ratio of the adjacent side to the hypotenuse in a right-angled triangle?

<p>Cosine</p> Signup and view all the answers

Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?

<p>Tangent</p> Signup and view all the answers

Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?

<p>Sine</p> Signup and view all the answers

In a right-angled triangle, if the length of the hypotenuse is 10 units and the length of the opposite side is 8 units, what is the value of the sine of the angle between the hypotenuse and the opposite side?

<p>0.8</p> Signup and view all the answers

If the length of the adjacent side in a right-angled triangle is 5 units and the length of the hypotenuse is 13 units, what is the value of the cosine of the angle between the adjacent side and the hypotenuse?

<p>0.75</p> Signup and view all the answers

Study Notes

Trigonometric Functions

  • The abbreviations sin, cos, and tan represent the sine, cosine, and tangent functions, respectively.
  • The sine function is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle.
  • The cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle.
  • The tangent function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

Applying Trigonometric Functions

  • If the length of the hypotenuse is 10 units and the length of the opposite side is 8 units, the value of the sine of the angle between the hypotenuse and the opposite side is 8/10 or 0.8.
  • If the length of the adjacent side is 5 units and the length of the hypotenuse is 13 units, the value of the cosine of the angle between the adjacent side and the hypotenuse is 5/13 or approximately 0.38.

Notation and Labeling

  • The angle is often labeled as θ (theta) in trigonometry.

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