Sin 47 Degrees — Value of sin(47°) and How to Find It

#Trigonometry
TL;DR
The value of sin 47 degrees is approximately 0.7314\mathbf{0.7314} — it is not a special-angle exact value, so there is no clean surd for it. This article shows how to find sin⁡47°\sin 47° honestly (calculator, the cofunction cos⁡43°\cos 43°, and table interpolation), gives the radian form, and places it on the unit circle.
BT
Bhanzu TeamLast updated on August 20, 20267 min read

The value of sin 47 degrees is approximately 0.73140.7314 (0.731353700.73135370 to eight places). Unlike sin⁡30°\sin 30° or sin⁡45°\sin 45°, the angle 47°47° is not a special angle, so sin⁡47°\sin 47° has no simple exact surd — it is read from a calculator, a trig table, or rewritten as the cofunction cos⁡43°\cos 43°.

Quick Answer:

Result: sin⁡47°≈0.7314\sin 47° \approx 0.7314

In radians: sin⁡(47π180)=sin⁡(0.82031)≈0.7314\sin\left(\frac{47\pi}{180}\right) = \sin(0.82031) \approx 0.7314

Notation: decimal approximation — 0.731353700.73135370 (8 dp)

Method shown: calculator (degree mode), the cofunction identity sin⁡47°=cos⁡43°\sin 47° = \cos 43°, and table interpolation

Exact form: none simple — 47°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°\sin 45° and sin⁡60°\sin 60°. The table below places it among its neighbours.

Angle (degrees)

Angle (radians)

sin⁡θ\sin\theta

Special angle?

30°30°

π6\frac{\pi}{6}

0.50000.5000

Yes (exact 12\tfrac{1}{2})

45°45°

π4\frac{\pi}{4}

0.70710.7071

Yes (22\tfrac{\sqrt2}{2})

46°46°

23π90\frac{23\pi}{90}

0.71930.7193

No

47°47°

47π180\frac{47\pi}{180}

0.73140.7314

No — decimal only

48°48°

4π15\frac{4\pi}{15}

0.74310.7431

No

60°60°

π3\frac{\pi}{3}

0.86600.8660

Yes (32\tfrac{\sqrt3}{2})

The nearest exact landmark is sin⁡45°=22≈0.7071\sin 45° = \frac{\sqrt2}{2} \approx 0.7071, and sin⁡47°\sin 47° sits just 0.02430.0243 above it.

What Does Sin 47 Degrees Mean?

Sine of an angle on the unit circle (radius 11, centred at the origin) is the yy-coordinate of the point at that angle, where every point is (cos⁡θ,sin⁡θ)(\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°47° lands in Quadrant I, where both coordinates are positive.

At 47°47° the radius has turned just past the 45°45° diagonal, so the point's height is a little above 0.70710.7071. That height — about 0.73140.7314 — is sin⁡47°\sin 47°.

How Do You Find the Value of Sin 47 Degrees?

Because 47°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)\sin(47) with the calculator in DEG mode.

sin⁡47°=0.73135370…≈0.7314\sin 47° = 0.73135370\ldots \approx 0.7314

In radian mode the same keystrokes give sin⁡(47 rad)≈0.1236\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⁡θ=cos⁡(90°−θ)\sin\theta = \cos(90° - \theta).

sin⁡47°=cos⁡(90°−47°)=cos⁡43°\sin 47° = \cos(90° - 47°) = \cos 43°

So sin⁡47°\sin 47° and cos⁡43°\cos 43° are the same number, 0.73140.7314. 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\sin 45° = 0.7071 and sin⁡50°=0.7660\sin 50° = 0.7660, estimate sin⁡47°\sin 47° by linear interpolation:

sin⁡47°≈0.7071+47−4550−45,(0.7660−0.7071)=0.7071+0.4(0.0589)=0.7307\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 0.0010.001 of the true 0.73140.7314 — 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 47π180≈0.8203\frac{47\pi}{180} \approx 0.8203 rad, but the value of the sine is the same number, ≈0.7314\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°\sin 47° to four decimal places.

From a calculator in degree mode, sin⁡47°=0.7314\sin 47° = 0.7314.

Example 2 (wrong path first)

Find sin⁡47°\sin 47° using a cofunction.

Wrong attempt. A student writes sin⁡47°=sin⁡(90°−47°)=sin⁡43°\sin 47° = \sin(90° - 47°) = \sin 43°.

Why it breaks. The cofunction of sine is cosine, not sine: sin⁡θ=cos⁡(90°−θ)\sin\theta = \cos(90° - \theta). Writing sin⁡43°\sin 43° gives 0.68200.6820, not 0.73140.7314 — the wrong value.

Correct. sin⁡47°=cos⁡(90°−47°)=cos⁡43°=0.7314\sin 47° = \cos(90° - 47°) = \cos 43° = 0.7314.

Example 3

A wire runs from the top of a 1010 m pole to the ground, making a 47°47° angle with the wire's straight length. How high is the attachment if the wire is 1010 m long?

Height =10×sin⁡47°=10×0.7314=7.314= 10 \times \sin 47° = 10 \times 0.7314 = 7.314 m.

Example 4

Compare sin⁡47°\sin 47° with sin⁡45°\sin 45°.

sin⁡45°=0.7071\sin 45° = 0.7071; sin⁡47°=0.7314\sin 47° = 0.7314. The extra 2°2° raises the value by 0.02430.0243, because sine is still climbing steeply near 45°45°.

Example 5

Verify sin⁡47°=cos⁡43°\sin 47° = \cos 43° on a calculator.

sin⁡47°=0.73135\sin 47° = 0.73135 and cos⁡43°=0.73135\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°\sin 47° as a complementary angle and keeping the same function.

Don't do this: writing sin⁡47°=sin⁡43°\sin 47° = \sin 43°.

The correct way: the complement of sine is cosine — sin⁡47°=cos⁡43°\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°\sin 43° and cos⁡43°\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°=22\sin 45° = \tfrac{\sqrt2}{2}.

Don't do this: trying to write sin⁡47°\sin 47° as a simple radical.

The correct way: 47°47° is not a special angle, so sin⁡47°\sin 47° is given as the decimal 0.73140.7314. 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\sin(47) = 0.1236 and reporting it as sin⁡47°\sin 47°.

The correct way: check DEG mode for sin⁡47°\sin 47°; 0.12360.1236 is sin⁡(47 radians)\sin(47\ \text{radians}), an angle of more than seven full turns.

Key Takeaways

  • Sin 47 degrees is approximately 0.73140.7314 — a decimal, not a clean surd.

  • 47°47° is not a special angle, so the value comes from a calculator, the cofunction cos⁡43°\cos 43°, or interpolation.

  • The cofunction identity sin⁡47°=cos⁡43°\sin 47° = \cos 43° gives the same number two ways.

  • In radians the angle is 47π180\frac{47\pi}{180}, but the sine value stays ≈0.7314\approx 0.7314.

  • sin⁡47°\sin 47° sits just 0.02430.0243 above sin⁡45°=0.7071\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

  1. State sin⁡47°\sin 47° to four decimal places.

  2. Rewrite sin⁡47°\sin 47° as a cosine using the cofunction identity, then check it on a calculator.

  3. Use sin⁡45°=0.7071\sin 45° = 0.7071 and sin⁡50°=0.7660\sin 50° = 0.7660 to interpolate sin⁡47°\sin 47°.

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Frequently Asked Questions

What is sin 47 degrees?
Approximately 0.73140.7314 (0.731353700.73135370 to eight places). It sits just above sin⁡45°=0.7071\sin 45° = 0.7071.
Is sin 47 degrees an exact value?
No. 47°47° is not a special angle, so sin⁡47°\sin 47° has no simple surd — it is a decimal approximation.
What is sin 47 degrees in terms of cos 43?
They are equal. By the cofunction identity, sin⁡47°=cos⁡(90°−47°)=cos⁡43°=0.7314\sin 47° = \cos(90° - 47°) = \cos 43° = 0.7314.
What is sin 47 degrees in radians?
The angle is 47π180≈0.8203\frac{47\pi}{180} \approx 0.8203 rad, but the sine value is unchanged at ≈0.7314\approx 0.7314.
Is sin 47 degrees positive or negative?
Positive. 47°47° is in the first quadrant, where sine is positive.
Do I need to memorise sin 47 degrees?
No. Non-special angles like 47°47° are not memorisation targets — you find them with a calculator, a cofunction, or a trigonometric table.
✍️ Written By
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Bhanzu Team
Content Creator and Editor
Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.
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