Consider the angle shown below that has a radian measure of θ. A circle with a radius of 3.2 cm is centered at the angle's vertex, and the terminal point is shown.

The terminal point's horizontal distance to the right of the center of the circle is __ times as large as the radius of the circle, and therefore:
cos(θ)=

The terminal point's vertical distance above the center of the circle is_ times as large as the radius of the circle, and therefore:
sin(θ)=

The sine and cosine of an angle are the ratio of the opposite side and adjacent side of the reference angle to the hypotenuse side respectively

The completed statement is presented as follows;

The terminal point's horizontal distance to the right of the center of the circle is 0.921875 times as large as the radius of the circle, and therefore: cos(θ) = 0.921875

The terminal point's vertical distance above the center of the circle is 0.390625 times as large as the radius of the circle, and therefore, sin(θ) = 0.390625

Reason:

Known parameters are;

The radius of the circle, R = 3.2 cm

The terminal point's horizontal distance to the right of center of the circle, x = 2.95 cm

The number of times x is larger than R, nₓ is given as follows;

[tex]n_x = \dfrac{2.95}{3.2} = 0.921875[/tex]

The number of times x is larger than R, nₓ = 0.921875

Therefore;

[tex]cos(\theta) =\dfrac{x}{R} = 0.921875[/tex]

cos(θ) = 0.921875

The terminal point's vertical distance above the center of the circle, y = 1.25 cm

The number of times y is larger than R, [tex]n_y[/tex], is given as follows;

[tex]n_y = \dfrac{1.25}{3.2} = 0.390625[/tex]

The number of times y is larger than R, [tex]n_y[/tex] = 0.390625

Therefore;

[tex]sin(\theta) =\dfrac{y}{R} = 0.390625[/tex]

sin(θ) = 0.390625

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