8 Questions
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?
Cosine
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
Tangent
Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle?
Sine
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?
0.8
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?
0.75
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.
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.
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