Chapter 8.1, Problem 22AYU

To determine

To find: The value of $\frac{\cos 40°}{\sin 50°}$.

Answer to Problem 22AYU

1

Explanation of Solution

Given:

$\frac{\cos 40°}{\sin 50°}$

Formula used:

$\cos \left(90°-\text{ A}\right)=\text{ sinA}$

Calculation:

By using complementary theorem

If $\text{A }+\text{ B }=90°$ then

$\cos \left(90°-\text{ A}\right)=\text{ sinA}$

That means the complementary function of $\text{sinA }=\text{ cosB}$

So $\cos 40°$ can written as $\cos \left(90°-\text{ 50}°\right)=\text{ sin50}°$

$\frac{\cos 40°}{\sin 50°}=\frac{\sin 50°}{\sin 50°}=1$