Question

If sin theta =5/13 where theta <90 degree ,find the value of tan theta + 1/cos theta

Answer 1

Given:

sin ∅=5/13 where ∅ <90°

To Find:

The value of tan ∅ + 1/cos ∅

Solution:

We know that

sin∅ = p/h = 5/13

$h^{2} = p^{2} + b^{2}$

So,

$b^{2} = h^{2} - p^{2}$

    $= 13^{2} - 5^{2}$

    = 169 - 25 = 144

$b = \sqrt{144}$ = 12

Also,

cos ∅ = b/h = 12 / 13

tan ∅  = p/b = 5/12

Now,

tan ∅ + 1/cos ∅ = $\frac{5}{12} + \frac{13}{12} = \frac{18}{12} = \frac{3}{2}$

Hence, the value of tan theta + 1/cos theta is  $\frac{3}{2}$