Question

If sin B = \(\frac {3}{5}\), then find sec B.

(a) \(\frac {3}{4}\)

(b) \(\frac {4}{5}\)

(c) \(\frac {5}{4}\)

(d) \(\frac {5}{3}\)

I have been asked this question in an interview for job.

The doubt is from Trigonometric Ratios in division Trigonometry of Mathematics – Class 10

Answer 1

Correct option is (c) \(\frac {5}{4}\)

The explanation: Sin B = \(\frac {Opposite \, side}{Hypotenuse} = \frac {3}{5}\)

From Pythagoras theorem, (Hypotenuse)^2 = (Opposite side)^2 + (Adjacent side)^2

5^2 = 3^2 + (Adjacent side)^2

(Adjacent side)^2 = 5^2 – 3^2

Adjacent side = √16 = 4

Sec B = \(\frac {Hypotenuse}{Adjacent \, side} = \frac {5}{4}\)