Final answer:
The correct method to solve for x in a sine function is by using trigonometric identities. The correct option is (c).
Step-by-step explanation:
The question is asking how one can solve for x within a sine function. Among the options A) Trial and error method, B) Factoring, C) Trigonometric identities, D) Quadratic formula, the correct method to solve for x in a sine function is using trigonometric identities along with inverse trigonometric functions.
To solve an equation involving a sine function, you would follow these steps:
- Identify the unknown and the known values in the equation.
- Choose an appropriate trigonometric identity if the equation is complex and can be simplified.
- If the equation is in the form sin(x) = number, take the inverse sine (also known as arc sine) of both sides to solve for x, ensuring that you consider all possible solutions depending on the range of x.
- Check your answer to see if it is reasonable and makes sense in the context of the problem.
The quadratic formula is relevant when you have a polynomial equation of the form ax²+bx+c = 0, and factoring is also a method for solving such quadratic equations. However, for equations solely involving sine functions and not polynomials, the quadratic formula and factoring are not the appropriate methods.