In the context of right triangle trigonometry, which trigonometric function is represented by the equation $x=a\sin wt$?

• A. Cosine
• B. Tangent
• C. Sine
• D. Secant

Answer: (C)

Verified step by step guidance

1. Identify the given equation: \(x = a \sin wt\). This shows that the variable \(x\) is expressed as a product of \(a\) and the sine of \(wt\).
2. Recall the definition of the sine function in right triangle trigonometry: \(\sin \theta = \frac{\text{opposite side}}{\text{hypotenuse}}\). The sine function relates an angle to the ratio of the side opposite the angle over the hypotenuse.
3. Recognize that the equation uses the sine function explicitly, which means it directly involves the sine of an angle or variable \(wt\).
4. Compare this with other trigonometric functions: cosine relates to adjacent over hypotenuse, tangent relates to opposite over adjacent, and secant is the reciprocal of cosine. Since the equation uses \(\sin\), it corresponds to the sine function.
5. Therefore, the trigonometric function represented by the equation \(x = a \sin wt\) is the sine function.