Chapter 8.1, Problem 19AYU

To determine

To find: The Value of $\text{sin38}°-\text{ cos}52°$.

Answer to Problem 19AYU

0

Explanation of Solution

Given:

$\text{sin38}°-\text{ cos}52°$

Formula used:

$\text{Sin}\left(90°-\text{ A}\right)=\text{ cosA}$

Calculation:

By using complementary theorem.

If $\text{A }+\text{ B }=90°$ then.

$\text{Sin}\left(90°-\text{ A}\right)=\text{ cosA}$

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

So $\text{sin38}°$ can written as $\text{Sin}\left(90°-52°\right)$.

$\text{Sin}\left(90°-52°\right)=\text{ cos}52°$

$\text{sin38}°-\text{ cos}52°=\text{ cos}52°-\text{ cos}52°=\text{ 0}$