Home » If (sin x° = frac{a}{b}), what is (sin (90 – x)°)?

If (sin x° = frac{a}{b}), what is (sin (90 – x)°)?

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})