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

Question

zloy xaker [14]

2 years ago

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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.

Mathematics

1 answer:

defon · Answer 1 · 2022-07-22T10:16:35+03:00

The abscissa of the ordered pair, that is the x-coordinate, is equal to 1 and the ordinate, the y-coordinate, is equal to -1. In the cartesian plane, this point lies in the fourth (IV) quadrant. The standard position of the angle is that which has one of its side is in the x-axis.

Solve for the hypotenuse of the right triangle formed.
h = sqrt((-1)² + (1)²) = √2
Below items show the calculation for each of the trigonometric functions.

sin θ = opposite/hypotenuse = y/h = (-1)/(√2) = -√2/2
cos θ = adjacent/hypotenuse = x/h = (1)/√2 = √2/2
tan θ = opposite/adjacent = y/x = -1/1 = -1