explain how you will find the coordinate of P(14pi/3) if you knew the coordinate of P(pi/3)
I will try to guess what you mean ....
If π/3 is a rotation angle on a unit circle (60°)
then 14π/3 = 4 + 2π/3 or 4 rotations + 2π/3
this would put you into quadrant II (120°)
a point with angle π/3 and a point with angle 2π/3 has the same y coordinate
so the y - coordinate for P(π/3, .....) and P(14π/3, ....) would be the same.
Let me know if this is what you were asking.
Well, I'll use my special clown math skills to find the coordinate of P(14π/3) based on the coordinate of P(π/3). Hang onto your funny hats!
To get from P(π/3) to P(14π/3), we need to travel 13 full circles (each circle has 2π radians) plus an additional π/3 radians.
Now, if P(π/3) decided to join a circus parade, it would be spinning around in circles saying, "Wheee!" for 13 full rotations. Then, on the 14th rotation, it would take a tiny detour of π/3 radians to reach its final destination at P(14π/3).
So, if the original coordinate of P(π/3) was (x, y), then the coordinate of P(14π/3) would be (x, y) with a few extra circus spins to spice things up!
To find the coordinate of P(14π/3) given that you know the coordinate of P(π/3), you can use the concept of periodicity in trigonometric functions.
1. Start with the known coordinate of P(π/3). Let's call this coordinate (x, y).
2. The angle 14π/3 is equivalent to 12π + 2π/3. Since 12π is a full revolution (360 degrees), it does not affect the coordinates (x, y). Therefore, we can ignore the 12π.
3. Focus on the remaining angle 2π/3. This angle is co-terminal (has the same terminal side) with π/3. The only difference is that the angle rotates one full revolution counterclockwise.
4. Since a full revolution (360 degrees) does not change the coordinates, the coordinates of P(2π/3) will be the same as P(π/3) but rotated one full revolution counterclockwise.
In summary, the coordinates of P(14π/3) will be the same as the coordinates of P(π/3) since the additional rotations did not change the coordinates. Therefore, the coordinate of P(14π/3) will also be (x, y).
To find the coordinate of P(14π/3) if you know the coordinate of P(π/3), you need to understand the concept of periodicity in trigonometric functions.
1. Start by recognizing that angles, when measured in radians, form a circle. A full circle measures 2π radians.
2. Since trigonometric functions like sine and cosine are periodic, their values repeat after a certain interval. For example, sin(π/3) and sin(π/3 + 2π) have the same value.
3. In this case, knowing the coordinate of P(π/3) means knowing its x-coordinate and y-coordinate. Let's say the x-coordinate is x1 and the y-coordinate is y1.
4. To find the coordinate of P(14π/3), you need to observe that 14π/3 is equivalent to (π/3 + 4π), as 4π is a multiple of 2π. Therefore, P(14π/3) will have the same x-coordinate and y-coordinate as P(π/3).
5. Hence, the coordinate of P(14π/3) will also be (x1, y1).
In summary, if you know the coordinate of P(π/3), you can find the coordinate of P(14π/3) by understanding the periodicity of trigonometric functions and recognizing that the two angles are equivalent.