Question

select the correct answer.

which trigonometric ratio will not have the same value as \\(\sin a\\)?

Explanation:

Determine the measure of angle A

$$ \angle A = 180^\circ - 90^\circ - 45^\circ = 45^\circ $$

Evaluate the target trigonometric ratio

$$ \sin A = \sin(45^\circ) = \frac{\sqrt{2}}{2} $$

Compare with other trigonometric ratios of the acute angles

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Answer:

Any trigonometric ratio that does not equal \(\frac{\sqrt{2}}{2}\) (such as \(\tan A\), \(\tan C\), \(\cot A\), \(\cot C\), \(\sec A\), \(\sec C\), \(\csc A\), or \(\csc C\)) will not have the same value as \(\sin A\).

Specifically, the primary ratios \(\tan A\) and \(\tan C\) equal \(1\), which is not equal to \(\sin A\).