Respuesta :
The sine of the angle theta is given by the ratio of the opposite leg to the hypotenuse side of the right triangle formed by the terminal segment.
- The true location of the terminal side of the angle θ is given by the option; Theta has a reference angle of 30° and is in Quadrant I or II.
Reasons:
The given parameters are;
The sine value of the given angle = One-half
Required: To select the true statement of the location of the terminal side.
Solution:
Given that sin(θ) = 0.5, we have;
The sine of an angle is positive in Quadrant I and Quadrant II
- Given that the value of sin(θ) is positive, we have θ is in Quadrant I or Quadrant II
The reference angle, is the angle formed between the angle's terminal side and x-axis
By trigonometric ratios, considering the reference angle, we have;
θ = arcsin(0.5) = 30°
Therefore;
The option that gives the true location of the terminal side of an angle, that have a sine value of One-half is; Theta has a reference angle of 30° and is in Quadrant I or II.
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