The value of sin 47 degrees is approximately $0.7314$ ($0.73135370$ to eight places). Unlike $\sin 30°$ or $\sin 45°$, the angle $47°$ is not a special angle, so $\sin 47°$ has no simple exact surd — it is read from a calculator, a trig table, or rewritten as the cofunction $\cos 43°$.
Quick Answer:
Result: $\sin 47° \approx 0.7314$
In radians: $\sin\left(\frac{47\pi}{180}\right) = \sin(0.82031) \approx 0.7314$
Notation: decimal approximation — $0.73135370$ (8 dp)
Method shown: calculator (degree mode), the cofunction identity $\sin 47° = \cos 43°$, and table interpolation
Exact form: none simple — $47°$ is not a special angle, so no clean radical exists
Quick Reference — Sine Near 47 Degrees
Sin 47° sits between the special landmarks $\sin 45°$ and $\sin 60°$. The table below places it among its neighbours.
Angle (degrees) | Angle (radians) | $\sin\theta$ | Special angle? |
|---|---|---|---|
$30°$ | $\frac{\pi}{6}$ | $0.5000$ | Yes (exact $\tfrac{1}{2}$) |
$45°$ | $\frac{\pi}{4}$ | $0.7071$ | Yes ($\tfrac{\sqrt2}{2}$) |
$46°$ | $\frac{23\pi}{90}$ | $0.7193$ | No |
$47°$ | $\frac{47\pi}{180}$ | $0.7314$ | No — decimal only |
$48°$ | $\frac{4\pi}{15}$ | $0.7431$ | No |
$60°$ | $\frac{\pi}{3}$ | $0.8660$ | Yes ($\tfrac{\sqrt3}{2}$) |
The nearest exact landmark is $\sin 45° = \frac{\sqrt2}{2} \approx 0.7071$, and $\sin 47°$ sits just $0.0243$ above it.
What Does Sin 47 Degrees Mean?
Sine of an angle on the unit circle (radius $1$, centred at the origin) is the $y$-coordinate of the point at that angle, where every point is $(\cos\theta, \sin\theta)$. Here a quadrant is one of the four regions the axes cut the plane into, numbered anticlockwise from the top right; $47°$ lands in Quadrant I, where both coordinates are positive.
At $47°$ the radius has turned just past the $45°$ diagonal, so the point's height is a little above $0.7071$. That height — about $0.7314$ — is $\sin 47°$.
How Do You Find the Value of Sin 47 Degrees?
Because $47°$ is not a special angle, there is no surd to simplify to. So how do you find sin 47 degrees without a calculator? You rewrite it as a cofunction or read it off a table — here are the three honest routes.
Method 1: Calculator (set to degree mode)
Type $\sin(47)$ with the calculator in DEG mode.
$$\sin 47° = 0.73135370\ldots \approx 0.7314$$
In radian mode the same keystrokes give $\sin(47\ \text{rad}) \approx 0.1236$ — a completely different number, so the mode matters.
Method 2: Cofunction identity
Sine and cosine are cofunctions: $\sin\theta = \cos(90° - \theta)$.
$$\sin 47° = \cos(90° - 47°) = \cos 43°$$
So $\sin 47°$ and $\cos 43°$ are the same number, $0.7314$. This is useful when a table or problem gives you cosines but you need a sine.
Method 3: Table interpolation
If a trig table lists $\sin 45° = 0.7071$ and $\sin 50° = 0.7660$, estimate $\sin 47°$ by linear interpolation:
$$\sin 47° \approx 0.7071 + \frac{47 - 45}{50 - 45},(0.7660 - 0.7071) = 0.7071 + 0.4(0.0589) = 0.7307$$
That lands within $0.001$ of the true $0.7314$ — close, though interpolation always carries a small error because the sine curve bends slightly between the table rows.
What is sin 47 degrees in radians?
The angle converts to $\frac{47\pi}{180} \approx 0.8203$ rad, but the value of the sine is the same number, $\approx 0.7314$. Converting the angle to radians does not change the sine; it only changes how the angle is labelled.
Examples Using Sin 47 Degrees
Example 1
State $\sin 47°$ to four decimal places.
From a calculator in degree mode, $\sin 47° = 0.7314$.
Example 2 (wrong path first)
Find $\sin 47°$ using a cofunction.
Wrong attempt. A student writes $\sin 47° = \sin(90° - 47°) = \sin 43°$.
Why it breaks. The cofunction of sine is cosine, not sine: $\sin\theta = \cos(90° - \theta)$. Writing $\sin 43°$ gives $0.6820$, not $0.7314$ — the wrong value.
Correct. $\sin 47° = \cos(90° - 47°) = \cos 43° = 0.7314$.
Example 3
A wire runs from the top of a $10$ m pole to the ground, making a $47°$ angle with the wire's straight length. How high is the attachment if the wire is $10$ m long?
Height $= 10 \times \sin 47° = 10 \times 0.7314 = 7.314$ m.
Example 4
Compare $\sin 47°$ with $\sin 45°$.
$\sin 45° = 0.7071$; $\sin 47° = 0.7314$. The extra $2°$ raises the value by $0.0243$, because sine is still climbing steeply near $45°$.
Example 5
Verify $\sin 47° = \cos 43°$ on a calculator.
$\sin 47° = 0.73135$ and $\cos 43° = 0.73135$ — identical, confirming the cofunction identity.
Sin 47 Degrees — Where Things Go Sideways
Most errors on a non-special angle come from a few repeatable habits, not from the arithmetic.
Mistake 1: Using the wrong cofunction
Where it slips in: rewriting $\sin 47°$ as a complementary angle and keeping the same function.
Don't do this: writing $\sin 47° = \sin 43°$.
The correct way: the complement of sine is cosine — $\sin 47° = \cos 43°$. The habit that fixes this is to circle the "co" and swap the function every time you swap to the complementary angle; a learner who keeps the function the same will be off by the gap between $\sin 43°$ and $\cos 43°$ on every problem.
Mistake 2: Hunting for an exact surd
Where it slips in: assuming every angle has a clean value like $\sin 45° = \tfrac{\sqrt2}{2}$.
Don't do this: trying to write $\sin 47°$ as a simple radical.
The correct way: $47°$ is not a special angle, so $\sin 47°$ is given as the decimal $0.7314$. The learner who has only memorised the special-angle table has to switch to a calculator, a cofunction, or interpolation here — and that is the honest answer, not a failure.
Mistake 3: Forgetting the calculator's angle mode
Where it slips in: the calculator was left in radian mode.
Don't do this: reading $\sin(47) = 0.1236$ and reporting it as $\sin 47°$.
The correct way: check DEG mode for $\sin 47°$; $0.1236$ is $\sin(47\ \text{radians})$, an angle of more than seven full turns.
Key Takeaways
Sin 47 degrees is approximately $0.7314$ — a decimal, not a clean surd.
$47°$ is not a special angle, so the value comes from a calculator, the cofunction $\cos 43°$, or interpolation.
The cofunction identity $\sin 47° = \cos 43°$ gives the same number two ways.
In radians the angle is $\frac{47\pi}{180}$, but the sine value stays $\approx 0.7314$.
$\sin 47°$ sits just $0.0243$ above $\sin 45° = 0.7071$.
To take sine values further with a teacher, explore Bhanzu's trigonometry tutor, a high school math tutor, or math classes online.
Practice These Before Moving On
State $\sin 47°$ to four decimal places.
Rewrite $\sin 47°$ as a cosine using the cofunction identity, then check it on a calculator.
Use $\sin 45° = 0.7071$ and $\sin 50° = 0.7660$ to interpolate $\sin 47°$.
Want a live trainer to walk through more sine-value problems? Book a free demo class.
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