Question 554017: the terminal arm of angle ϴ passes through the point R(-15,-8)
determine the distance from the origin to point R
determine the exact value of sin ϴ to the nearest tenth of a degree
can you please answer those 2 questions, i am stuck on them and can you show your work so i can learn from them,
thank you
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the terminal arm of angle ϴ passes through the point R(-15,-8)
Draw a line segment connecting (0,0) and (-15,-8)
That is the hypotenuse of a right triangle with sides equal
to 15 and 8
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determine the distance from the origin to point R
Use Pythagoras:
d = sqrt[15^2+8^2] = 17
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determine the exact value of sin ϴ to the nearest tenth of a degree
sin(theta) = opposite/hypotenuse = -8/17 =-0.4706
theta = sin^-1(-8/17) = 180-28.07 = 151.9 degrees
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Cheers,
Stan H.
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the terminal arm of the angle passes through the point (-15,-8).
this means that the value of x is equal to -15 and the value of y is equal to -8.
this forms a right triangle where the hypotenuse is equal to sqrt(-8)^2 + (-15)^2 = sqrt(289) which equals 17.
the hypotenuse is always positive, no matter which quadrant it is in.
the angle is in quadrant 3.
solve for the absolute value of the angle in this triangle.
sine of the angle is equal to -8/17.
get the arcsine of this for an angle of -28.07248694.
take the absolute value of this to get an angle of 28.07248694.
since this angle is in quadrant 3, the angle you are looking for is 180 degrees plus this angle which equals 208.07248694 degrees which rounds to 208.1 degrees.
see the attached diagram for a picture of what this looks like:
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