Question

cos2 θ The transformationPez, cos θ sin θ 2 gives the orthogonal projection of the vector,2 onto ortho cosesin θ sin2 θ | the line through the origin that makes the angle θ with the x-axis. Find the projection of'l,6] onto the line through the origintht makes an angle Give your answer to 2 decimal places. The vector- 334,103 Preview Points possible: 1 Unlimited attempts. Score on last attempt: 0. Score in gradebook: 0 Message instructor about this question Post this question to forum License

Answer 1

By the problem description, the projection is

By the problem description, the projection is P_pi/6 [1, 6]^T = (cos^2 pi/6 cos pi/6 sin pi/6 cos pi/6 sin pi/6 sin^2 pi/6) (1 6) = (3/4 squareroot 3/4 squareroot 3/4 1/4) (1 6) = (3 + 6 squareroot 3/4 6 + squareroot 3/4) Up to two decimal place, this is (3.35 1.93)^T

Up to two decimal place, this is $\begin{align*}\begin{pmatrix}3.35 & 1.93\end{pmatrix}^T\end{align*}$ .