Using Trigonometric Identities
Trig Identities
- \(x=\sin(t)+2\)
- \(y=\cos (t)-3\)
- \(\sin^2t+\cos^2t=1\)
- \(x=\sin (t)+2\to \sin t=x-2\)
- \(y=\cos(t)-3\to \cos t=y+3\)
- \(\sin^2t+\cos^{2}t=1\to (x-2)^2+(y+3)^2=1\)
- This equation is a circle ^^^^
\(x=2\sin t\), \(y=1-\cos^{2}t\)
- Find a cartesian equation for this parametric equation in the form \(y=f(x)\), \(-k\leq x\leq k\)
- \(1-\cos^2t=1-\cos^2t+\sin^2t\)
- \(=2\sin^2t\)
- \(y=\frac{1}{2}x^2\)
\(x=2\sin t\)
Max value of \(\sin t=-1 \text{ and }1\)
Max values of \(2\sin t=-2\text{ and }2\)