Question

on the following unit circle, \thetaθtheta is in radians. a unit circle with an angle from the positive x-axis to a ray labeled theta. the point where the ray intersects the circle is labeled 0.54, 0.84 and is in the first quadrant.

Answer 1

The value of the trigonometry are sin(Π-Ɵ) = 0.84 and sin(Π + Ɵ) = -0.84

According to the question, there is a circle whose radius is 1 and the ray intersects the circle at point (0.54, 0.84).

We need to find the trigonometric values, that is

 sin(Π-Ɵ) = sin(Ɵ) as we know that when the angle is in third quadrant sin is positive.

 sin(Π+Ɵ) = -sin(Ɵ) as we know that when the angle is in fourth quadrant sin is negative.

Also note that,  sinƟ = perpendicular/hypotenuse

Perpendicular = 0.84 as the perpendicular length will be equal to the length of the y-axis

Hypotenuse = 1 as the hypotenuse will be the radius of the circle which is formed by the ray.

Thus, sinƟ = 0.84/1 = 0.84

Hence, sin(Π-Ɵ) = 0.84

  And sin(Π+Ɵ) = -0.84

Learn more about trigonometry here : brainly.com/question/13729598

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