Question 660148: The terminal side of angle θ in standard position contains the points (-5,-12) give the cos θ.
Found 2 solutions by stanbon, math-vortex:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The terminal side of angle theta in standard
position contains the points (-5,-12) give the cos Theta .
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Since x = -5 and y = -12, r = sqrt[5^2 + 12^2] = sqrt(169) = 13
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cos(theta) = x/r = -5/13
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Cheers,
Stan H.
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website!
Hi, there--
The Problem:
The terminal side of angle θ in standard position contains the points (-5,-12) give the
cos θ.
Solution:
We can find the cosine of an angle in a right triangle if we know the length of the adjacent
side and the length of the hypotenuse.
Angle θ is in Quadrant III because both x and y are negative.
Since (-5,-12) is on the terminal side of the angle θ, we can draw a right triangle with
angle θ at the origin.
The hypotenuse of the triangle is the line segment from (0,0) to (-5,-12).
The side adjacent to angle θ is the horizontal line segment along the x-axis between
(0,0) and (-5,0). The directed side length is a=-5 units.
The side opposite angle θ is the vertical line segment between (-5,0) and (-5,-12). The
directed side length is b=-12 units.
Use the Pythagorean Equation to find the length of the hypotenuse c.
a^2 + b^2 = c^2
(-5)^2 + (-12)^2 =c^2
25 + 144 = c^2
169 = c^2
c = 13
cos(θ) = [directed length of adjacent side] / [directed length of hypotenuse]
cos(θ) = -12/13
If this is unclear, or you still have questions, please email me.
Mrs. Figge
math.in.the.vortex@gmail.com
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