Final answer:
To express sin O as a fraction in simplest form, we need the angle's measure and then can use trigonometric ratios or a calculator to find its value. The fraction must then be reduced to its simplest form by following algebraic rules, such as having the same quantity in the numerator and denominator equaling 1.
Step-by-step explanation:
To express sin O as a fraction in simplest form, we would need additional information, such as the value of the angle O or the context within which this question is asked. Generally, the value of sin O depends on the measure of angle O. For example, if O is 30 degrees, then sin O would be 0.5 (which is 1/2 in fraction form). If O is 45 degrees, then sin O would be √2/2, and if O is 60 degrees, then sin O would be √3/2.
For angles that are not commonly memorized, you may need to use a trigonometric table or a calculator to find the decimal value and then convert it into a fraction. Moreover, the fraction should be reduced to simplest form by eliminating common factors from the numerator and the denominator, as long as we perform the same operation on both sides of the equality, as per the rules of algebra.
To solve an equation, it is often useful to simplify and then perform operations to maintain equality. Negative exponents, for instance, indicate division or placement in the denominator. Moreover, a fraction that has the same quantity in the numerator as it has in the denominator simplifies to a value of 1.