Linear combinations

• July 22nd 2010, 06:20 AM
wiseguy
Linear combinations
The graph of y = cos (x - 1.3) is a sinusoid with a phase displacement of 1.3 radians.
Given that cos 1.3 ≈ 0.27 and sin 1.3 ≈ 0.96, write y as a linear combination of cos x and sin x.

My responce:

$y=cosxcos1.3+sinxsin1.3$

I'm new to linear equations so I want to make sure I'm doing this correctly...
• July 22nd 2010, 07:34 AM
Failure
Quote:

Originally Posted by wiseguy
The graph of y = cos (x - 1.3) is a sinusoid with a phase displacement of 1.3 radians.
Given that cos 1.3 ≈ 0.27 and sin 1.3 ≈ 0.96, write y as a linear combination of cos x and sin x.

My responce:

$y=cosxcos1.3+sinxsin1.3$

I'm new to linear equations so I want to make sure I'm doing this correctly...

Looks ok to me. However, you haven't made use of the given values of of cos and sin for the argument 1.3. So the expected answer seems to be:

$y\approx 0.27\cos x+0.96\sin x$