question 3 (4 points)\nexpress the equation y = sin(x - 30°) using the cosine function. you may have to…
question 3 (4 points)\nexpress the equation y = sin(x - 30°) using the cosine function. you may have to graph the function to show your work.
Answer
Explanation:
Step1: Recall the trigonometric identity
We know that $\sin(A)=\cos(A - 90^{\circ})$. Let $A=x - 30^{\circ}$.
Step2: Substitute into the identity
$y=\sin(x - 30^{\circ})=\cos((x - 30^{\circ})-90^{\circ})$.
Step3: Simplify the expression
$(x - 30^{\circ})-90^{\circ}=x-120^{\circ}$. So $y = \cos(x - 120^{\circ})$.
Answer:
$y=\cos(x - 120^{\circ})$