When you are given a resultant and an angle, what strategy should you use to find the components?

Understand the Problem

The question is asking about the method to use in trigonometry when given a resultant vector and an angle, specifically what strategy is appropriate for finding its components.

Answer

B) Sin and Cos

Steps to Solve

Identify the Trigonometric Function To find the components of a resultant vector, you typically use the sine and cosine functions based on the angle provided.
Determine the Components Using the angle $\theta$ of the resultant vector and its magnitude $R$, the components can be calculated using:
- The horizontal component: $$ R_x = R \cdot \cos(\theta) $$
- The vertical component: $$ R_y = R \cdot \sin(\theta) $$
Understand the Use of Pythagorean Theorem The Pythagorean theorem ($a^2 + b^2 = c^2$) is useful for finding the magnitude of the resultant when you have the component values. However, it is not used to find the components from the magnitude and direction.
Clarify the Role of Tangent The tangent function relates the angle to the opposite and adjacent sides in a right triangle, but for finding components directly from the resultant and angle, sine and cosine are the primary functions used.

The strategy you should use to find the components is B) Sin and Cos.

More Information

Using sine and cosine to find the components of a vector is foundational in trigonometry. The sine function relates to the opposite side, while the cosine relates to the adjacent side, which helps in breaking down the resultant vector into its components.

Tips

Relying on Tangent: Some may mistakenly think tangent is used directly to find components; it's primarily used to find angles or ratios between sides.
Misapplying Pythagorean Theorem: It's important to remember that the Pythagorean theorem is for calculating the magnitude of the resultant when you have the components, not for determining the components from the resultant.

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