Duration: 3:40

147 views

0

If coordinate system \( x y \) is being rotated through an angle \( \theta \) in anti clock wise direction about the origin as shown in the diagram, Coordinates of \( P(x, y) \) has been change to \( P(X, Y) \) in new coordinate system \( X Y \), then \( \mathrm{x}, \mathrm{y}, \mathrm{X}, \mathrm{Y} \) are related as given below.
\( \mathrm{P} \)
W
\[
\begin{aligned}
X & =x \sec \theta+(y-x \tan \theta) \sin \theta & \text { and } & Y=(y-x \tan \theta) \cos \theta \\
& =x \sec \theta+y \sin \theta-\frac{x \sin ^{2} \theta}{\cos \theta} & & =y \cos \theta-x \sin \theta \\
- & X & =x \cos \theta+y \sin \theta & Y=-x \sin \theta+y \cos \theta
\end{aligned}
\]
- If the axes are rotated through \( 60^{\circ} \) in anticlockwise direction about origin. Find co-ordinats of point \( (2,6) \) in new co-ordinate axes.
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live