Cosine Reference Table Near 25 Degrees
Twenty-five degrees is a non-standard angle, so its cosine is a decimal rather than a clean radical. The standard angles around it are exact, while $25°$ is read off a calculator or the unit circle — here is the neighbourhood in degrees and radians.
Angle (degrees) | Angle (radians) | $\cos\theta$ | Exact form? |
|---|---|---|---|
$0°$ | $0$ | $1.0000$ | yes ($1$) |
$25°$ | $\dfrac{5\pi}{36}$ | $0.9063$ | no |
$30°$ | $\dfrac{\pi}{6}$ | $0.8660$ | yes ($\frac{\sqrt{3}}{2}$) |
$45°$ | $\dfrac{\pi}{4}$ | $0.7071$ | yes ($\frac{\sqrt{2}}{2}$) |
$60°$ | $\dfrac{\pi}{3}$ | $0.5000$ | yes ($\frac{1}{2}$) |
$90°$ | $\dfrac{\pi}{2}$ | $0.0000$ | yes ($0$) |
Cos 25° sits just above cos 30° because cosine shrinks as the angle grows, and $25°$ is a touch smaller than $30°$. That sandwiching — between $\cos 0° = 1$ and $\cos 30° \approx 0.866$ — is a quick sanity check on the $0.9063$ value.
Where Cos 25 Degrees Shows Up
A 25° angle is a common roof pitch — gentle enough to shed water, shallow enough to walk on — and the horizontal span of a rafter at that pitch scales with $\cos 25°$. The same value sizes the base of a ramp or a staircase stringer cut at $25°$, and it appears in optics, where light at a $25°$ angle of incidence reflects according to cosine-weighted terms.
Surveyors reading a slope of $25°$ multiply the slope distance by $\cos 25° \approx 0.9063$ to recover the true horizontal distance, the same trigonometric ratio used in any incline measurement. That value is the $x$-coordinate of the $25°$ point on the unit circle.
What Cos 25 Degrees Means
Cosine is one of the three core trigonometric functions. In a right triangle, the cosine of an angle is the side adjacent to it divided by the hypotenuse, so $\cos 25°$ is the fraction of the hypotenuse taken up by the adjacent side in a right triangle with a $25°$ angle.
On the unit circle — a circle of radius $1$ centred at the origin — cosine is the $x$-coordinate of the point where the angle's radius meets the circle. At $25°$ that point is approximately $(0.9063, 0.4226)$, and because $25°$ falls in Quadrant I both coordinates are positive, so $\cos 25° \approx 0.9063$.
How Do You Find the Value of Cos 25 Degrees?
Unlike $30°$ or $45°$, the angle $25°$ has no neat closed form, so the practical answer is a decimal. Three routes get you there.
Method 1: Reference angle and quadrant
Since $25°$ is already acute and in Quadrant I, it is its own reference angle, and cosine is positive there:
$$\cos 25° = +0.9063$$
The reference angle only does heavy lifting for angles past $90°$; for $25°$ it confirms the positive sign.
Method 2: Unit circle / calculator
Set the calculator to degree mode and enter $\cos(25)$:
$$\cos 25° = 0.9063078\ldots$$
This matches the $x$-coordinate of the unit-circle point at $25°$.
Method 3: Estimate from neighbouring identities
You can bracket the value without a table: because $25°$ lies between $0°$ and $30°$, its cosine lies between $\cos 30° \approx 0.866$ and $\cos 0° = 1$, so $\cos 25°$ must be a little above $0.866$ — and $0.9063$ fits. For a closer estimate, the identity $\cos 25° = \sqrt{1 - \sin^2 25°}$ gives the value once $\sin 25° \approx 0.4226$ is known.
Examples of Cos 25 Degrees
Example 1
Evaluate $10\cos 25°$, rounded to two decimals.
$$10 \times 0.9063 = 9.063 \approx 9.06$$
Example 2
A surveyor reads a slope distance of $50$ m up a $25°$ incline. Find the horizontal distance.
Wrong attempt. A student multiplies by $\sin 25° \approx 0.4226$, getting $50 \times 0.4226 = 21.13$ m.
That gives the vertical rise, not the horizontal run — a $25°$ slope is shallow, so the horizontal distance should be close to the full $50$ m, not less than half of it.
Correct. Horizontal distance uses the adjacent side, so it is the cosine:
$$50 \times \cos 25° = 50 \times 0.9063 = 45.3 \text{ m}$$
Example 3
Find $\cos 25°$ given $\sin 25° \approx 0.4226$, using the Pythagorean identity.
$$\cos 25° = \sqrt{1 - \sin^2 25°} = \sqrt{1 - 0.4226^2} = \sqrt{1 - 0.1786} = \sqrt{0.8214} \approx 0.9063$$
The Pythagorean identity recovers the value from sine.
Example 4
Express $25°$ in radians.
$$25° \times \frac{\pi}{180°} = \frac{25\pi}{180} = \frac{5\pi}{36} \approx 0.4363 \text{ radians}$$
So $\cos\left(\frac{5\pi}{36}\right) \approx 0.9063$.
Example 5
A ladder leans against a wall, making a $25°$ angle with the wall and reaching $9$ m up it. How long is the ladder?
The $9$ m vertical reach is the side adjacent to the $25°$ angle at the top, so $\cos 25° = \frac{9}{\text{ladder}}$. Solving, ladder $= \frac{9}{\cos 25°} = \frac{9}{0.9063} \approx 9.93$ m.
Where Students Trip Up on Cos 25 Degrees
Mistake 1: Hunting for an exact radical form
Where it slips in: Treating $25°$ like a standard angle and trying to write $\cos 25°$ as a clean square-root expression.
Don't do this: Forcing $\cos 25° = \frac{\sqrt{\text{something}}}{2}$ to mimic $\cos 30°$.
The correct way: $25°$ has no simple exact form, so the decimal $0.9063$ is the answer.
Mistake 2: Calculator in radian mode
Where it slips in: A calculator left in radian mode returns $\cos(25) \approx 0.9912$, which looks plausible but is wrong.
Don't do this: Entering $\cos(25)$ without checking the mode.
The correct way: Confirm degree mode; $\cos 25° = 0.9063$. When a Bhanzu trainer sees an off value like $0.99$, the first check is always the angle-mode indicator.
Mistake 3: Swapping cosine and sine on a slope problem
Where it slips in: Word problems where horizontal and vertical components get mixed.
Don't do this: Using $\sin 25°$ for the horizontal run.
The correct way: The horizontal (adjacent) component uses cosine. A shallow $25°$ slope keeps most of its length horizontal, so the cosine factor $0.9063$ — close to $1$ — is the sanity check.
Key Takeaways
Cos 25 degrees is approximately $0.9063$, a positive decimal because $25°$ is a Quadrant I, non-standard angle.
There is no simple radical form — the value comes from the unit circle or a calculator in degree mode.
In radians, $\cos 25° = \cos\left(\frac{5\pi}{36}\right)$.
A quick check: $\cos 25°$ sits just above $\cos 30° \approx 0.866$ and below $\cos 0° = 1$.
Quick Self-Check - Try These
Evaluate $8\cos 25°$ to two decimals.
A $25°$ ramp covers a slope distance of $12$ m. Find its horizontal run using $\cos 25°$.
Convert $25°$ to radians and confirm $\cos\left(\frac{5\pi}{36}\right) \approx 0.9063$ on a calculator.
Want a live Bhanzu trainer to walk through more cos 25 degrees problems? Book a free demo class — online globally.
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