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Given:
The point (9,-12) is on terminal side of angle theta in standard position.
To find:
The exact value of each of the six trigonometric functions of theta.
Solution:
The given point is (9,-12). Here, x-coordinate is positive and y-coordinate is negative. So, the point lies in 4th quadrant and only cos and sec are positive in 4th quadrant.
We know that,
Now,
Therefore, the values of six trigonometric functions of theta are .
The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
<h3>What is a Scale Factor ?</h3>The ratio by which the new image is bigger or smaller than the original image is the scale factor.
It is given that
Triangle A″B″C″ is formed using the translation (x + 0, y + 2)
and the dilation by a scale factor of 2 from the origin.
coordinate plane with triangle ABC at A (- 3, 3), B (1, - 3), and C (- 3, -3).
segment AC is equal to A''C'' over 2
Scale factor = 2
The coordinates are
A (- 3, 3), B (1, - 3), and c (- 3, -3) is translated using (x + 2, y + 0),
new coordinates
A'(- 1, 3), B'(3, - 3), and C'(- 1, -3).
The dilation by a scale factor of from the origin
A″ (-2, 6), B″ (6, -6) and C″(-2, -6)
By the distance formula
AB =
A''B'' = = 2
Therefore
AB = A''B'' /2
Similarly AC = A''C'' /2
The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
To know more about Scale Factor
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