paulinaserrano2010
contestada

An angle's initial ray points in the 12-o'clock direction and the terminal ray rotates CCW. Let θ represent angle's varying measure (in radians).
a. If θ=0.5 what is the slope of the terminal ray?
b.Write an expression (in terms of θ) that represents the varying slope of the terminal ray.

Respuesta :

The slope of the rotating terminal ray with the initial ray at 12-O'clock is

given by the cotangent of the angle of rotation.

  • a. The slope of the terminal ray when θ = 0.5 is approximately -1.830
  • b. The slope of the terminal ray is given by the expression, -cot(θ)

Reasons:

The direction of the initial ray =  12-O'clock direction

The direction of rotation of the terminal ray = CCW

θ = The measure of the angle formed by the terminal ray

a. Required:

The value of the slope of the terminal ray when θ = 0.5

Solution;

The slope is the ratio of the rise to the run of the terminal ray, which is

given by the tangent of the angle made by the terminal ray with the

horizontal, as follows;

The angle the terminal ray makes with the horizontal =  [tex]\left(0.5 + \dfrac{\pi}{2} \right)[/tex]

[tex]\therefore \mathrm{The \ slope \ of \ the \ terminal \ line } = tan \left(0.5 + \dfrac{\pi}{2} \right) = -cot(0.5) \approx \underline{-1.830}[/tex]

b. The slope is the tangent the terminal ray makes with the horizontal,

therefore, the expression in terms of θ that represents the varying slope is

presented as follows;

[tex]\mathrm{The \ expression \ for \ the \ varying \ slope \ of \ the \ terminal \ ray} = tan \left(\theta + \dfrac{\pi}{2} \right) = \underline{ -cot(\theta)}[/tex]

Learn more here:

https://brainly.com/question/20619188

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