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An angle in standard position measures pi/2 radians, and P(0, 1) is on the terminal side of the angle. What is the value of the cosine of this angle
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Respuesta :

meerkat18
Angles could be expressed in degrees or in radians. The relationship between the two could be easily explained by illustrating a circle. A semi-circle has a total angle of 180°. This is equal to a π radians. So if the angle is π/2, in degrees, that would be 180/2 = 90°. 

Then, determining the cosine 90° in a calculator would yield an answer of zero.

The value of the cosine of the angle pi/2 is given by cosine ratio of the

sides that form the angle.

Correct response;

  • The correct option for the cosine of the angle is; 0

How to find the cosine of an angle using trigonometric ratios?

Given;

The measure of the angle = [tex]\mathbf{\dfrac{\pi}{2}}[/tex]

The coordinate of the point on the terminal side of the angle is P(0, 1)

Required;

The cosine of the angle

Solution;

From trigonometric ratios, we have;

  • [tex]Cosine \ of \ angle = \mathbf{\dfrac{Length \ of \ adjacent}{Length \ of \ hypotenuse\ side}}[/tex]

The length of hypotenuse = Distance from the origin to point P, which is given as follows;

The length of hypotenuse = [tex]\mathbf{\sqrt{1^2 + 0^2}}[/tex] = 1

Therefore;

[tex]Cosine \ of \ angle, \ \mathbf{cos\left(\dfrac{\pi}{2} \right)}= \dfrac{0}{1} = 0[/tex]

  • The value of the cosine of the angle, pi/2 radians is; 0

Learn more about the cosine of an angle here:

https://brainly.com/question/16955719

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