Question 1114151: The point P(-3,-6) lies on the terminal arm of an angle θ in standard position.
a) Determine the exact values of sin θ, cos θ and tan θ.
b) Determine the principal angle, θ.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! we are given P(-3,-6) on the terminal arm
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this puts theta in the third quadrant
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using Pythagorean Theorem with h as the hypotenuse
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(-3)^2 + (-6)^2 = h^2
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h^2 = 9 + 36 = 45
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h = 3 * square root(5)
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Note in this case theta = 180 + reference angle(alpha), alpha is always measured over the closest distance to the x axis
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a) sin alpha = -6/3 * square root(5) = -2/square root(5)
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cos alpha = -3/3 * square root(5) = -1/square root(5)
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tan alpha = -6/-3 = 2
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b) tan^(-1) 2 = 63.4349 degrees
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theta = 180 + 63.4349 = 243.4349 degrees
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Note -sin alpha = sin theta, -cos alpha = cos theta and tan alpha = tan theta, that is, the sin and cos are negative in the third quadrant and the tan is positive
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