Question

It is saying this is the wrong answer and I genuinely do not know what I am doing wrong. Please help and do not give me the answer I already have

3. 3.32/5 points | Previous Answers BoyceDiffEQ10 3.7.004 My Notes Ask Your Teacher Determine ω0, R, and δ so as to write the given expression in the form u-R cos(aot-8). () 8 arctan

Answer 1

U = R cos (w_0 t - delta) rightarrow (1) Now u = -2 cos pi t - 3 sin pi t Rightarrow u = squareroot (-2)^2 + (-3)^2 (-2 cos pi t - 3 sin pi t/squareroot (-2)^2 + (-3)^2) Rightarrow u = squareroot 4 + 9 (-2 cos pi t - 3 sin pi t/squareroot 4 + 9) Rightarrow u = squareroot 13 (-2 cos pi t - 3 sin Pi t/squareroot 13) Rightarrow u = squareroot 13 (-2/squareroot 13 cos pi t - 3/squareroot 13 sin pi t) rightarrow (II) Now suppose cos theta = -2/squareroot 13 for some theta elementof [0, 2 pi] Now sin^2 theta = 1 - cos^2 theta Rightarrow sin^2 theta = 1 - (-2/squareroot 13)^2 Rightarrow sin^2 theta = 1 - 4/13 Rightarrow sin^2 theta = 13 -4/13 Rightarrow sin^2 theta = 9/13 Rightarrow sin theta = plusminus 3/ Rightarrow 13 \r\n If we take theta between Pi to 3 pi/2 then Sin theta = -3/squareroot 13