Here is the graph of the function \( y = \sin(2x + 30^\circ) \), showing the sinusoidal wave with a frequency and phase shift based on the equation.

Would you like more details or have any questions about this function?

Here are 5 related questions to deepen your understanding:
1. How does the factor of 2 in \( \sin(2x) \) affect the frequency of the sine wave?
2. What role does the \( +30^\circ \) (or phase shift) play in modifying the sine function?
3. Can you find the amplitude of the function \( y = \sin(2x + 30^\circ) \)?
4. How would the graph change if the equation were \( y = \cos(2x + 30^\circ) \)?
5. What are the x-intercepts of this function?

**Tip:** Phase shifts move the graph horizontally. Positive shifts move the graph left, while negative shifts move it right.

Explore the graph of y = sin(2x + 30°), a trigonometric function that demonstrates frequency and phase shift. This detailed solution will guide you through how the sine wave changes with a frequency factor of 2 and a phase shift of +30°. Suitable for high school students in Grades 10-12.

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