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Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The terminal point is (1.33,−2).


What is the angle's measure (in radians)?
θ=
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Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The terminal point is (1.33,−2).W class=

Answer :

Answer:

5.3 or (4217pi/2500)

Step-by-step explanation:

Create a right triangle with the coordinates provided.

We can ignore the negative sign and create the equation

[tex]tan(x) = \frac{1.33}{2} [/tex]

x = 33.624

We then add 270 and x together because the coordinates are in the 4th quadrant.

angle = 303.624

To convert to radians, we multiply this number by pi/180

5.3 radians

xero099

The measure of the angle is approximately [tex]1.687\pi[/tex] radians.

By trigonometry we can determine the direction of the terminal ray ([tex]\theta[/tex]), in radians, by the following inverse trigonometric function:

[tex]\theta = \tan^{-1}\frac{y}{x}[/tex] (1)

Since [tex]x > 0[/tex], [tex]y <0[/tex] and angle is in standard position, the angle must have a direction greater than [tex]\frac{3\pi}{2}[/tex] radians and less than [tex]2\pi[/tex] radians. Hence, we conclude that direction of the angle is:

[tex]\theta = \tan^{-1} \left(\frac{-2}{1.33} \right)[/tex]

[tex]\theta \approx 1.687\pi\, rad[/tex]

The measure of the angle is approximately [tex]1.687\pi[/tex] radians.

We kindly invite to check this question on angles: https://brainly.com/question/18060525

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