Question$$g(x)=-2 \cos \left(\frac{1}{3}\left(x+20^{\circ}\right)\right)+4$$ e. State the equation of the axis of the curve f. State the amplitude g. State the period h. Does this sinusoidal function have a plase stifs to the lef or righte?

Studdy Solution
To determine the phase shift, we look at the expression inside the cosine function, $\frac{1}{3}(x + 20^\circ)$. The phase shift is determined by solving $bx + c = 0$.
Here, $c = \frac{1}{3} \times 20^\circ = \frac{20^\circ}{3}$.
The phase shift is:
$$x + 20^\circ = 0 \Rightarrow x = -20^\circ$$
Since the shift is negative, the function is shifted to the left.
e. The equation of the axis of the curve is $y = 4$.
f. The amplitude is $2$.
g. The period is $1080^\circ$.
h. The sinusoidal function has a phase shift to the left by $20^\circ$.