find the value for the indicated trig function for ø, if ø is an angle in standard position with the terminal side defined by the given point. (18,24); find cos ø
recall that cosine = x/r
And, r^2 = x^2+y^2
r^2 = 18^2+24^2
..
r = 30
cosØ = x/r = 18/30 = 3/5
To find the value of cosine for the angle ø, given that ø is an angle in standard position with the terminal side defined by the point (18,24), we can use the Pythagorean theorem and the concept of the unit circle.
First, let's label the coordinates of the given point (18,24) on a Cartesian plane. The x-coordinate represents the horizontal distance (18), and the y-coordinate represents the vertical distance (24).
Next, we can use the Pythagorean theorem to find the hypotenuse of the right triangle formed. By applying the theorem:
hypotenuse^2 = x^2 + y^2
We can substitute the values:
hypotenuse^2 = 18^2 + 24^2
hypotenuse^2 = 324 + 576
hypotenuse^2 = 900
Now, taking the square root of both sides, we get:
hypotenuse = √900
hypotenuse = 30
Since we are looking for the cosine of the angle ø, which is defined as the ratio of the adjacent side (x-coordinate) to the hypotenuse, we can conclude:
cos ø = x-coordinate / hypotenuse
cos ø = 18 / 30
Finally, simplifying the fraction:
cos ø = 3 / 5
So, the value of cos ø for the given angle ø is 3/5.