Final Answer:
The equation of a sine graph can be represented by y = sin(x), thus the correct option is A.
Step-by-step explanation:
A sine graph is a type of graph that shows the relationship between an angle and the ratio of the length of the side opposite that angle to the length of the hypotenuse in a right triangle. In mathematical terms, this ratio is known as the sine function, which is denoted by sin(x). Therefore, the equation of a sine graph is given by y = sin(x), where x represents the angle and y represents the ratio.
To better understand this equation, let us consider an example. Suppose we want to graph the sine function for the angle x = π/6. We can use the equation y = sin(x) to determine the corresponding value of y. Plugging in x = π/6, we get y = sin(π/6) = 1/2. This means that when x = π/6, y = 1/2, and this point can be plotted on the graph. Similarly, we can calculate the values of y for other angles and plot them on the graph to get a complete sine graph.
In addition to representing the equation of a sine graph, y = sin(x) can also be used to solve trigonometric equations. For example, if we are given the value of y and want to find the corresponding angle x, we can rearrange the equation to get x = sin⁻¹(y). This inverse sine function allows us to find the angle when the ratio is known.
In conclusion, the equation of a sine graph can be written as y = sin(x), where x represents the angle and y represents the ratio of the side opposite to the hypotenuse in a right triangle. This equation can be used to graph the sine function as well as to solve trigonometric equations.
Complete Question:
Explain the equation that represents a sine graph and justify the correct option among the given choices:
A) y = sin(x)
B) y = cos(x)
C) y = tan(x)
D) y = csc(x)