Question

select the correct answer. which trigonometric ratio will not have the same value as sin a?

Explanation:

Answer:

Since in right - triangle \(ABC\) with \(\angle B = 90^{\circ}\) and \(\angle C=45^{\circ}\), then \(\angle A = 45^{\circ}\). \(\sin A=\frac{BC}{AC}\), \(\cos A=\frac{AB}{AC}\), \(\tan A=\frac{BC}{AB}\), \(\csc A=\frac{AC}{BC}\), \(\sec A=\frac{AC}{AB}\), \(\cot A=\frac{AB}{BC}\). The trigonometric ratio that will not have the same value as \(\sin A\) is \(\cos A\) (because \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\) and \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\) in an isosceles right - triangle, but in general for an angle \(A\) in a right - triangle, \(\sin A\) and \(\cos A\) are different except for \(A = 45^{\circ}\)). So if we assume non - special cases or consider the general relationship between trigonometric functions, we can say \(\cos A\). If this is a multiple - choice question and we assume the options are standard trigonometric ratios:
If the options are:
A. \(\cos A\)
B. \(\csc A\)
C. \(\tan A\)
D. \(\cot A\)
The answer is A. \(\cos A\)