If (sin x° = frac{a}{b}), what is (sin (90 – x)°)?
-
A.
(frac{sqrt{b^2 – a^2}}{b}) -
B.
1(frac{-a}{b}) -
C.
(frac{b^2 – a^2}{b}) -
D.
(frac{a^2 – b^2}{b}) -
E.
(sqrt{b^2 – a^3})
Correct Answer: Option A
Explanation
(sin x = frac{a}{b})
(sin^{2} x + cos^{2} x = 1)
(sin^{2} x = frac{a^{2}}{b^{2}})
(cos^{2} x = 1 – frac{a^{2}}{b^{2}} = frac{b^{2} – a^{2}}{b^{2}})
(therefore cos x = frac{sqrt{b^{2} – a^{2}}}{b})
(sin (90 – x) = sin 90 cos x – cos 90 sin x)
= ((1 times frac{sqrt{b^{2} – a^{2}}}{b}) – (0 times frac{a}{b}))
= (frac{sqrt{b^{2} – a^{2}}}{b})