206 STEP 4. Review the Knowledge You Need to Score High
- Whenx=5 sint=5,t=
π
2
,so
y= 1 −cos
π
2=1.
- Ifu=〈6,− 1 〉andv=〈−4, 3〉,4〈6,− 1 〉
− 3 〈−4, 3〉=〈24,− 4 〉+〈12,− 9 〉=
〈36,− 13 〉. - Replaceθwith−θ. 2 sin(− 4 θ)=
−2 sin(4θ)/=2 sin(4θ), so the graph is not
symmetric about the polar axis. Replaceθ
withπ−θ. 2 sin(4(π−θ))=2 sin(4π− 4 θ)
= 2 [sin 4πcos 4θ−sin 4θcos 4π]=
−2 sin 4θ/=2 sin 4θ, so the graph is not
symmetric about the linex=
π
2. Replace
θwithθ+π.
2 sin(4(θ+π))=2 sin(4θ+ 4 π)=
2 [sin 4θcos 4π+cos 4θsin 4π]=2 sin 4θ,
so the graph is symmetric about the pole.
35. The magnitude of the vector 3∥ i+ 4 jis
∥ 3 i+ 4 j∥∥=√ 32 + 42 =5.