Question

express the following as a function of a single angle.
sin 340° cos 120° − cos 340° sin 120°
sum & difference formulas
sine and cosine
cos(a ± b) =
cosacosb ∓ sinasinb
sin(a ± b) =
sinacosb ± cosasinb
options:
sin 220°
cos 220°
cos 460°
sin 460°

Explanation:

Step1: Identify the formula

We use the sine difference formula: $\sin(A - B) = \sin A \cos B - \cos A \sin B$.
Here, $A = 340^\circ$ and $B = 120^\circ$.

Step2: Apply the formula

Substitute $A = 340^\circ$ and $B = 120^\circ$ into the formula:
$\sin(340^\circ - 120^\circ) = \sin 340^\circ \cos 120^\circ - \cos 340^\circ \sin 120^\circ$

Step3: Calculate the angle

Calculate $340^\circ - 120^\circ = 220^\circ$.
So, $\sin 340^\circ \cos 120^\circ - \cos 340^\circ \sin 120^\circ = \sin(220^\circ)$

Answer:

$\sin 220^\circ$ (corresponding to the option "sin 220°")