What is the ratio for sin a expressed as a fraction in its simplest form?

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The sine function, denoted as sin(a), is a fundamental function in trigonometry that describes the ratio of the length of the side opposite an angle a in a right-angled triangle to the length of the hypotenuse of the triangle. When expressed as a fraction, sin(a) is represented as:

  • sin(a) = \frac{opposite}{hypotenuse}

To simplify this concept further:

  1. The opposite side is the side that is directly across from angle a.
  2. The hypotenuse is the longest side of the right triangle, opposite the right angle.

For example, if we have a right triangle where:

  • The length of the side opposite to angle a is 3 units.
  • The length of the hypotenuse is 5 units.

We can express sin(a) as:

sin(a) = \frac{3}{5}

This fraction \frac{3}{5} is already in its simplest form, meaning that 3 and 5 have no common factors other than 1.

In conclusion, the ratio for sin(a) is simply the ratio of the side opposite angle a to the hypotenuse, written as a fraction in its simplest form.

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