Find the sin angle between two 2d vectors

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SUMMARY

The discussion focuses on calculating the sine angle between two 2D vectors, specifically vector U=<1, 3> and vector V=<5, 2>. The user is familiar with finding cos(theta) but seeks guidance on determining sin(theta). The formula provided for sin(theta) is derived from the Pythagorean identity: sin(theta) = √(1 - cos²(theta)). This method allows for the calculation of sin(theta) once cos(theta) is known, ensuring accurate results for the angle between the vectors.

PREREQUISITES
  • Understanding of basic trigonometric functions
  • Familiarity with vector notation and operations
  • Knowledge of the Pythagorean identity in trigonometry
  • Ability to calculate cos(theta) for vectors
NEXT STEPS
  • Learn how to calculate cos(theta) using the dot product of vectors
  • Study the properties of 2D vectors in trigonometry
  • Explore the application of the Pythagorean identity in various contexts
  • Practice solving problems involving angles between vectors
USEFUL FOR

Students preparing for math tests, particularly in trigonometry and vector analysis, as well as educators seeking to clarify concepts related to angles between vectors.

Elissa89
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Tomorrow is my math test and I'm going over the study guide:

I have vector U=<1, 3> and vector V=<5, 2>

It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)?

I already know how to find the missing angle for cos(theta) but we never covered how to find the missing angle for sin(theta). It was never in our homework and it's not in my notes but apparently it could be on the test.

So if someone could give me the formula and then show a step by step on how to do this it would be most appreciated.
 
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Once you know \(\cos(\theta)\), then given \(0\le\theta\le\pi\), we may use a Pythagorean identity:

$$\sin(\theta)=\sqrt{1-\cos^2(\theta)}$$
 

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