Question

# Analysis of the voltage in a hairdryer involves terms of the form \sin(nwt-90^{\circ}), where n is a positive integer, w is the frequency of the volta

Limits and continuity

Analysis of the voltage in a hairdryer involves terms of the form$$\sin(nwt-90^{\circ})$$, where n is a positive integer, w is the frequency of the voltage, and t is time. Use an identity to simplify this expression.

$$\displaystyle{\sin{{\left(\alpha-\beta\right)}}}={\sin{\alpha}}{\cos{\beta}}-{\cos{\alpha}}{\sin{\beta}}$$
$$\displaystyle{\sin{{\left({n}{w}{t}-{90}^{{\circ}}\right)}}}={\sin{{\left({n}{w}{t}\right)}}}{\cos{{\left({90}^{{\circ}}\right)}}}-{\cos{{\left({n}{w}{t}\right)}}}{\sin{{\left({90}^{{\circ}}\right)}}}={\sin{{\left({n}{w}{t}\right)}}}{\left({0}\right)}-{\cos{{\left({n}{w}{t}\right)}}}{\left({1}\right)}=-{\cos{{\left({n}{w}{t}\right)}}}$$