Question

Given sin⁡θ=1/2 determine the value of sec θ. 0°<θ<90°

Answer 1

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 $\frac{2\sqrt{3}}{3}$. (Right choice: A)

How to determine the exact value of a given trigonometric function based on a known value

By trigonometry, we understand that the sine is defined by the following function:

$\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}$      (1)

Where:

• y - Opposite leg
• x - Adjacent leg

And the function secant is defined by:

$\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}$     (2)

If we know that x² + y² = 4 and y = 1, then we find that the secant is:

x² + 1 = 4

x² = 3

$x = \sqrt{3}$

Secant is postive for 0° < θ < 90°, thus:

$\sec \theta = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$

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 $\frac{2\sqrt{3}}{3}$. (Right choice: A)

To learn more on trigonometric functions: brainly.com/question/6904750

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