This graph represents a sine wave. Based on the periodic nature and shape of the curve, which starts at zero, increases to 1, decreases to -1, and returns to zero, it can be identified as the graph of the sine function.

Sine Function Formula:

$y = \sin(x)$

Let's locate the points $a, b, c, d, e, f$, which are typically placed at key points on the graph. These are usually the x-intercepts, peaks, and troughs of the sine wave.

1. Point a: This is the starting point of the graph.

   • Coordinates: $a(-360^\circ, 0)$.

2. Point b: This is the first peak, where the sine wave reaches its maximum value.

   • Coordinates: $b(-270^\circ, 1)$.

3. Point c: This is the x-intercept after the first peak.

   • Coordinates: $c(-180^\circ, 0)$.

4. Point d: This is the trough, where the sine wave reaches its minimum value.

   • Coordinates: $d(0^\circ, -1)$.

5. Point e: This is the next x-intercept.

   • Coordinates: $e(180^\circ, 0)$.

6. Point f: This is the next peak after point e.

   • Coordinates: $f(270^\circ, 1)$.

Thus, the points are:

• $a(-360^\circ, 0)$
• $b(-270^\circ, 1)$
• $c(-180^\circ, 0)$
• $d(0^\circ, -1)$
• $e(180^\circ, 0)$
• $f(270^\circ, 1)$

Would you like to go into more details or have any further questions?

Related Questions:

1. What is the amplitude of this sine function?
2. How would the graph change if the amplitude were doubled?
3. What is the period of the sine wave, and how is it calculated?
4. How would the graph shift if we added a phase shift of $90^\circ$?
5. How can we derive the equation of the sine function from this graph?

Tip:

Remember, for any sine or cosine function, the graph’s period is $360^\circ$ or $2\pi$ radians. The period tells you how often the function repeats itself.