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 which mathematical strategy to use in order to find the components of a vector when given a resultant and an angle.
Answer
B: Sin and Cos.
Answer for screen readers
The correct strategy to use when given a resultant and an angle to find the components is B: Sin and Cos.
Steps to Solve
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Identify the components needed
To find the components of a vector given a resultant (magnitude) and an angle, we typically need to break the vector down into its horizontal ($x$) and vertical ($y$) components. -
Use Trigonometric Functions
The most common strategy involves using sine and cosine functions, which relate the angles of a right triangle to the ratios of its sides.- The horizontal component ($x$) can be found using the cosine function: $$ x = R \cdot \cos(\theta) $$
- The vertical component ($y$) can be found using the sine function: $$ y = R \cdot \sin(\theta) $$
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Conclusion on strategy
Since the question lists options A, B, and C, the appropriate choice for this vector component problem is B, which includes both sine and cosine.
The correct strategy to use when given a resultant and an angle to find the components is B: Sin and Cos.
More Information
Using sine and cosine functions helps in breaking down a vector into its components based on the angle it makes with the horizontal axis. This method is widely used in physics and engineering for vector analysis.
Tips
- Confusing sine and cosine functions: Remember that cosine is used for the adjacent side (horizontal component) and sine for the opposite side (vertical component).
- Failing to input the angle in the correct mode (degrees or radians) based on your calculator's setting can lead to incorrect values.
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