If A + B = 90° and cos B=35, what is the value of sin A?

Question:

If $A+B=90^{\circ}$ and $\cos B=\frac{3}{5}$, what is the value of $\sin A$ ?

Solution:

We have:

$A+B=90^{\circ}$

$\cos B=\frac{3}{5}$

$A+B=90^{\circ}$

$\Rightarrow A=90^{\circ}-B$

$\Rightarrow \sin A=\sin \left(90^{\circ}-B\right)$

$\Rightarrow \sin A=\cos B$

$\Rightarrow \sin A=\frac{3}{5}\left[\sin \left(90^{\circ}-B\right)=\cos B\right]$

Hence the value of $\sin A$ is $\frac{3}{5}$