MHB Find the sin angle between two 2d vectors

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To find the sine angle between two 2D vectors, first calculate cos(theta) using the dot product formula. Once cos(theta) is known, apply the Pythagorean identity sin(theta) = sqrt(1 - cos^2(theta)) to determine sin(theta). This method allows for the calculation of the sine angle without needing direct access to sine values. Understanding this relationship is crucial for solving problems involving angles between vectors. Mastering these concepts will aid in preparing for the math test.
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:

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

Thread 'Area of Overlapping Squares'

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