Question

The point P(k, 24) is 25 units from the origin. If P is on the terminal arm of an angle in standard position, find, the value of k with the cosine of the angle.

Answer 1

first find k by pythagoras
\[k^2+24^2=25^2\]
\[k=\sqrt{25^2-24^2}=\sqrt{49}=7\]

Answer 2

actually k could also be -7, but i guess we are supposed to assume it is positive

Answer 3

now we can find the sine and cosine using the familiar right triangle ratios

\[\sin(\theta)=\frac{24}{25}\]
\[\cos(\theta)=\frac{7}{25}\] etc

Answer 4

@alexeis_nicole you got this?

Answer 5

@satellite73 ye and the back of my book says that k = +-7/24 ... it might just be wrong on the 24 part