Find the angle between 2 vectors w=i+3j, vector v=<5, 2>

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SUMMARY

The discussion focuses on calculating the angle between two vectors, specifically vector w = i + 3j and vector v = <5, 2>. The participants confirm the method for finding cos(theta) using the dot product and magnitudes of the vectors. To find sin(theta), the Pythagorean identity is applied, specifically using the formula sin(t) = √(1 - cos²(t)). This approach solidifies the relationship between sine and cosine in vector analysis.

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I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>
 
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Elissa89 said:
I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

find the cosine, then use a form of the Pythagorean identity ...

$\sin{t} = \sqrt{1-\cos^2{t}}$
 

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