If sinα=3/5 and α is acute, find the value of sec(90°-α).

If $sin α = \frac{3}{5}$ and $α$ is acute, find the value of $sec (9 0^{\circ} - α)$ .

hard MCQ 2 marks Class 10 · Mathematics · Introduction to Trigonometry

$\frac{5}{3}$
$\frac{3}{5}$
$\frac{5}{4}$
$\frac{4}{3}$

Answer

\frac{5}{3}

The correct answer is $\frac{5}{3}$ — The secant is the reciprocal of cosine: $sec (9 0^{\circ} - α) = \frac{1}{c o s ( 9 0 ^{\circ} - α )} = \frac{1}{\frac{3}{5}} = \frac{5}{3}$ .

Step-by-step solution

For complementary angles, $cos (9 0^{\circ} - α) = sin α$ . Thus $cos (9 0^{\circ} - α) = \frac{3}{5}$ .
The secant is the reciprocal of cosine: $sec (9 0^{\circ} - α) = \frac{1}{c o s ( 9 0 ^{\circ} - α )} = \frac{1}{\frac{3}{5}} = \frac{5}{3}$ .

Common mistake: Taking

sec

1/ sin

of the complement instead of

1/ cos

Concept tested: Complementary angle identity and reciprocal function

Published 22 August 2026 · How this solution was prepared and checked

If sinα=53​ and α is acute, find the value of sec(90∘−α).

Step-by-step solution

Related questions

If $sin α = \frac{3}{5}$ and $α$ is acute, find the value of $sec (9 0^{\circ} - α)$ .