The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
2 answers:
Graphing the given point takes us to quadrant 4. Drop a perpendicular to the point (1, -1) and draw a line from the origin to the point. This line is the hypotenuse.
Let h = hypotenuse
(-1)^2 + (1)^2 = h^2
1 + 1 = h^2
2 = h^2
Taking the square root on both sides of the equation we get
sqrt{2} = h
In quadrant 4, only cosine is positive.
sine θ = -1/sqrt{2}
cos θ = 1/sqrt{2}
tan θ = -1/1
tan θ = -1
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