Cos 270 Degrees = 0 — Value, Unit Circle, Radians

Quick Answer:

• Result: $\cos 270° = 0$

• Notation: $\cos\left(\dfrac{3\pi}{2}\right) = 0$ (radians)

• Method shown: unit circle — the $x$-coordinate at three-quarters of a turn

• Approximate value: $0$ (exact)

• Exact form: $0$

A rotation of $270°$ — three-quarters of the way around the unit circle, or $\frac{3\pi}{2}$ radians — lands on the point at the very bottom, $(0, -1)$. Cosine reads the $x$-coordinate of where you land, and at the bottom of the circle that $x$-coordinate is $0$. The point sits directly below the center, so it has no horizontal offset at all.

Quick Reference Table — Cosine of Standard Angles

This table lists cosine at the standard angles in both degrees and radians, with $270°$ highlighted.

Cosine crosses zero twice per turn — at $90°$ and again at $270°$. Both are points where the circle is at its top or bottom, directly above or below the center, with no horizontal distance from the $y$-axis.

Where cos 270 Degrees Appears

The value $\cos 270° = 0$ marks a quarter-cycle turning point in any oscillation. In a cosine wave modelling a swinging pendulum or an AC voltage, the moment the phase reaches $270°$ is when the horizontal cosine component is exactly zero and the motion is passing through its midline.

The same zero defines the vertical axis in screen and robotics geometry: a heading of $270°$ points straight down, with no left-right component, which is why navigation and robotics control systems treat $270°$ as a pure-vertical bearing. Wherever a rotating quantity has "no horizontal part," $\cos 270° = 0$ is the number saying so.

What is cos 270 Degrees?

Cosine of an angle is, on the unit circle, the $x$-coordinate of the point reached by rotating that angle counterclockwise from the positive $x$-axis. A turn of $270°$ covers three of the four quarter-turns.

That rotation lands on $(0, -1)$ — the lowest point of the circle. The $x$-coordinate there is $0$, so $\cos 270° = 0$. Written in radians the angle is $\frac{3\pi}{2}$, which is why $\cos 270°$ and $\cos\left(\frac{3\pi}{2}\right)$ are the same number.

How To Find The Value of cos 270 Degrees

Method 1 — Unit circle

Rotate $270°$ counterclockwise from $(1, 0)$. Three quarter-turns put you at the bottom of the circle, the point $(0, -1)$.

Cosine is the $x$-coordinate of that point.

Final answer: $\cos 270° = 0$.

Method 2 — Cosine subtraction formula

Write $270°$ as $360° - 90°$ and apply $\cos(A - B) = \cos A\cos B + \sin A\sin B$:

$$\cos(360° - 90°) = \cos 360°\cos 90° + \sin 360°\sin 90°$$

$$= (1)(0) + (0)(1) = 0$$

Final answer: $\cos 270° = 0$.

Method 3 — Co-function shift

Use $\cos(270°) = \cos(180° + 90°) = -\cos 90°$ via the periodic shift, and $\cos 90° = 0$:

$$\cos 270° = -\cos 90° = -(0) = 0$$

Zero has no sign, so the negative in front changes nothing here.

Common mistakes with cos 270 degrees

Mistake 1: Confusing cos 270° with sin 270°

Where it slips in: At $270°$ the unit-circle point is $(0, -1)$, and the two coordinates get swapped.

Don't do this: Writing $\cos 270° = -1$ (that is $\sin 270°$, the $y$-coordinate).

The correct way: Cosine is the $x$-coordinate, so $\cos 270° = 0$; sine is the $y$-coordinate, so $\sin 270° = -1$.

This swap is the recurring trap on quadrantal angles — a Mathway unit-circle walkthrough for $\cos 270°$ exists precisely because so many learners reach for $-1$.

Mistake 2: Calculator in degree vs radian mode

Where it slips in: Typing cos(270) while the calculator is set to radians.

Don't do this: Reading $\cos(270 \text{ rad}) \approx 0.984$ and reporting it as $\cos 270°$.

The correct way: Use degree mode for $\cos 270°$, or enter $\cos\left(\frac{3\pi}{2}\right)$ in radian mode. Both give $0$.

Mistake 3: Writing 0 with a sign

Where it slips in: Carrying the second-quadrant intuition that "cosine is negative here" into the answer.

Don't do this: Writing $\cos 270° = -0$ or treating the result as a small negative number.

The correct way: The result is exactly $0$ — zero has no sign, so $\cos 270° = 0$, plain.

Conclusion

• Cos 270 degrees equals $0$ — the cosine of three-quarters of a turn, written $\cos\left(\frac{3\pi}{2}\right)$ in radians.

• The rotation lands on $(0, -1)$, the bottom of the unit circle, where the $x$-coordinate is $0$.

• Three routes agree: unit circle, the subtraction formula on $360° - 90°$, and the co-function shift.

• The most common slip is swapping cosine and sine — $\cos 270° = 0$, $\sin 270° = -1$.

Quick self-check — try these

1. Evaluate $\cos 270° + \sin 270°$.

2. Write $\cos 270°$ in radians and state its value.

3. Explain in one sentence why $\cos 270°$ and $\cos 90°$ are equal.

If #1 didn't give $-1$, recheck the coordinates of the point at $270°$. Want a live Bhanzu trainer to walk through more unit-circle problems? Book a free demo class — online globally.