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An angle's initial ray points in the

3
-o'clock direction and its terminal ray rotates counterclockwise. Let
θ
represent the angle's measure (in radians).

If
θ
=
0.5
, what is the terminal ray's slope?



If
θ
=
1.81
, what is the terminal ray's slope?



Write an expression (in terms of
θ
) that represents the terminal ray's slope.

User Hessam
by
7.4k points

1 Answer

4 votes

To find the terminal ray's slope, use the sine function and the trigonometric property of the tangent function. The expression for the terminal ray's slope is slope = sin(θ). For θ = 0.5, the slope is sin(0.5) ≈ 0.4794. Similarly, for θ = 1.81, the slope is sin(1.81) ≈ 0.9723.

The expression (in terms of θ) that represents the terminal ray's slope is slope = sin(θ).

To find the terminal ray's slope, we can use the trigonometric property that the tangent function gives the ratio of the y-coordinate to the x-coordinate of a point on the unit circle. Since the initial ray points in the 3-o'clock direction, the x-coordinate is 1. When the angle measure is θ = 0.5 radians, the x-coordinate remains unchanged, but the y-coordinate changes.

The y-coordinate can be found using the sine function: y = sin(θ). The slope of the terminal ray is then given by the ratio of the y-coordinate to the x-coordinate: slope = sin(θ) / 1 = sin(θ).

For θ = 0.5, the slope is sin(0.5) ≈ 0.4794. Similarly, for θ = 1.81, the slope is sin(1.81) ≈ 0.9723.

The expression (in terms of θ) that represents the terminal ray's slope is slope = sin(θ).

User Elacuesta
by
7.3k points