A 15-degree counterclockwise rotation about (4,6) transforms (2,1) onto another point (x,y). Find x and y correct to the three decimal places.

Pls find attached work. I know I am doing something wrong but i can't figure it out.

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- Jun 9th 2011, 09:22 PMVeronica1999rotation
A 15-degree counterclockwise rotation about (4,6) transforms (2,1) onto another point (x,y). Find x and y correct to the three decimal places.

Pls find attached work. I know I am doing something wrong but i can't figure it out. - Jun 9th 2011, 09:42 PMsa-ri-ga-ma
Let O (4, 6) be the center. Let A be ( 2,1) and B be ( x, y). Draw a vertical line from O. Draw perpendiculars AD and BE from A and B on the vertical line. Let the angle AOD be θ. Then then angle BOE is equal to ( 15 + θ) degrees. Take tanθ and tan(15 + θ) and proceed.

- Jun 9th 2011, 10:48 PMVeronica1999
Thank you for your help.

i was not sure how to apply tan so I used cos and sin.

Is my answer correct? And could you show me how to use tan?

pls find attached work.

thanks in advance for your time. - Jun 10th 2011, 02:22 AMsa-ri-ga-ma
Your answer is correct. From the figure you can see that AD = (4-2) and OD = (6- 1).

so tanθ = 2/5 = 0.4.