Math Problem Statement
Solution
To solve the given problem:
We need to resolve the vector into its -component and -component. The angle given is , measured counterclockwise from the positive x-axis.
Formula:
- The -component of the vector is:
- The -component of the vector is:
Steps:
- Substitute and into the formulas.
- Compute the values for and using a calculator or trigonometric table.
- Perform the calculations:
Final Answer:
- (rounded to the nearest tenth)
- (rounded to the nearest tenth)
Let me know if you would like further clarification or a more detailed explanation.
Here are five related questions:
- What happens to the components if the angle is in a different quadrant?
- How can we verify the results using a vector diagram?
- What are the differences between polar and Cartesian coordinate representations?
- Can we calculate the magnitude of a vector from its components?
- How does the sine and cosine of an angle determine the direction of the components?
Tip: Always visualize the angle relative to the coordinate axes to confirm the signs of the components!
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Math Problem Analysis
Mathematical Concepts
Vector resolution
Trigonometry
Components of a vector
Formulas
Ax = A * cos(θ)
Ay = A * sin(θ)
Theorems
Trigonometric functions of a vector angle
Suitable Grade Level
Grades 10-12
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