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

AI Thread Summary
To find the angle between vectors w = i + 3j and v = <5, 2>, first calculate the cosine of the angle using the dot product formula. The cosine can be derived from the formula cos(θ) = (w · v) / (||w|| ||v||). Once the cosine is determined, the sine can be found using the Pythagorean identity sin(θ) = √(1 - cos²(θ)). This method allows for the complete determination of the angle between the two vectors. Understanding both sine and cosine is essential for solving problems involving vector angles.
Elissa89
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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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