By applying the concepts of trigonometric functions and given that sin θ = 1/2 and 0° < θ < 90°, then the value of the secant of the given angle is [tex]\frac{2\sqrt{3}}{3}[/tex]. (Right choice: A)
By trigonometry, we understand that the sine is defined by the following function:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
Where:
And the function secant is defined by:
[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (2)
If we know that x² + y² = 4 and y = 1, then we find that the secant is:
x² + 1 = 4
x² = 3
[tex]x = \sqrt{3}[/tex]
Secant is postive for 0° < θ < 90°, thus:
[tex]\sec \theta = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}[/tex]
By applying the concepts of trigonometric functions and given that sin θ = 1/2 and 0° < θ < 90°, then the value of the secant of the given angle is [tex]\frac{2\sqrt{3}}{3}[/tex]. (Right choice: A)
To learn more on trigonometric functions: https://brainly.com/question/6904750
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