Sine and cosine trace the same wave — they differ only in where that wave begins. Both rise and fall between −1 and 1, and both complete one full cycle every 360°.

Graph One cycle of each curve

Concept Where each curve starts

sin θ

starts at 0 when θ = 0°

maximum 1 at 90°

back to 0 at 180°

minimum −1 at 270°

cos θ

starts at 1 when θ = 0°

reaches 0 at 90°

minimum −1 at 180°

back to 0 at 270°

On the unit circle $\sin\theta$ is the vertical coordinate $y$ and $\cos\theta$ is the horizontal coordinate $x$ . Cosine simply runs 90° ahead of sine: $\cos\theta = \sin(\theta + 90°)$ — same shape, different starting point.

Concept Amplitude

\text{amplitude} = \frac{\text{maximum} - \text{minimum}}{2}

For both curves the maximum is 1 and the minimum is −1.

\dfrac{1 - (-1)}{2} = \dfrac{2}{2}

⟹ amplitude = 1

The subtraction matters: a curve can be shifted up or down, so the amplitude is half the distance between top and bottom, not simply the maximum value.

Reference The two curves side by side

Property	sin θ	cos θ
Starting value	0 at θ = 0°	1 at θ = 0°
Maximum	1 at 90°	1 at 0°
Minimum	−1 at 270°	−1 at 180°
Amplitude	1	1
Period	360° = 2π	360° = 2π
On the unit circle	the y-coordinate	the x-coordinate

Summary

sin θ is the y-coordinate on the unit circle and starts at 0; cos θ is the x-coordinate and starts at 1.
Both have period 360° = 2π radians.
Amplitude = (maximum − minimum) ÷ 2 = 1, so values run from −1 to 1.
cos θ = sin(θ + 90°): cosine leads sine by a quarter cycle.

Sine and Cosine — Period and Amplitude