If P ( t ) = ( cos ⁡ t , sin ⁡ t ) has coordinates (0.949,0.316), find the coordinates of

Question

1. P(t+pi)
2. x= ____ y=______
3. P(-t)
4. x=_____ y=_______
5. P(t-pi)
6. x= ____ y=______
7. P(-t-pi)
8. x= ____ y=______

Answer 1

It is not necessary to find the angle. Start by plotting the given point on a graph: (0.949,0.316)

In all cases, the x and y values are the same--only the signs are changed

1. P(t+pi): This moves the angle from the 1st quadrant to the 3rd, so both signs are changed: (-0.949,-0.316)
2. P(-t): moves the angle to the 4th quadrant: the x value is the same, and the sign of y is reversed: (0.949,-0.316)
3. P(t-pi): Same as #1
4. P(-t-pi): Moves #2 from the 4th quadrant to the 2nd: (-0.949,-0.316)

Answer 2

radians; pi=180°

x=acos.949*cos(asin.316)=18.377*.948=17.436

y= 18.377 * .316 =5.807

180+17.436=197.436

180+5.807=185.307