## 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?

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

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

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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?

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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?

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## 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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