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1 answer:
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Given:
Point (7,12) is rotated 1260° counterclockwise about the origin.
To find:
The x-coordinate of the point after this rotation.
Solution:
If a point is rotated 360 degrees then its coordinates remains unchanged.
If a point is rotated 180 counterclockwise about the origin degrees, then
We know that,
After rotation the coordinates of points remains same, i.e., (7,12). So, after that (7,12) is rotated 180° counterclockwise about the origin.
The point (7,12) becomes (-7,-12) after rotation of 1260° counterclockwise about the origin.
Therefore, the x-coordinate of the required point is -7.
Step-by-step explanation:
First factor out the negative sign from the expression and reorder the terms
That's
<u>Using trigonometric </u><u>identities</u>
That's
<h3><u>Rewrite the expression</u>
That's
We have
<h3><u>Rewrite the second fraction</u>
That's
<h3>Since they have the same denominator we can write the fraction as
Using the identity
<h3><u>Rewrite the expression</u>
We have
<h3><u>Using the trigonometric identity</u>
<h3><u>Rewrite the expression</u>
That's
<h3>Which is
<h3><u>Using the trigonometric identity</u>
<h3>Rewrite the expression
That's
<h3><u>Simplify the expression using symmetry of trigonometric functions</u>
That's
<h3><u>Remove the parenthesis </u>
We have the final answer as
<h2>As proven
Hope this helps you