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

## TL;DR
The value of sin 47 degrees is approximately 0.7314 — it is not a special-angle exact value, so there is no clean surd for it. This article shows how to find \( \sin 47° \) honestly (calculator, the cofunction \( \cos 43° \), and table interpolation), gives the radian form, and places it on the unit circle.

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 12)          |
| 45°              | \( \frac{\pi}{4} \)             | 0.7071                             | Yes (\( \frac{\sqrt{2}}{2} \)) |
| 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 (\( \frac{\sqrt{3}}{2} \)) |

The nearest exact landmark is \( \sin 45° = \frac{\sqrt{2}}{2} \approx 0.7071 \), and \( \sin 47° \) sits just 0.0243 above it.

## What Does Sin 47 Degrees Mean?
Sine of an angle on the [unit circle](/content/math/geometry/unit-circle/index.html) (radius 1, centered 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.
\( \sin 47° = 0.73135370… \approx 0.7314 \)
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](/content/math/trigonometry/cofunction-identities/index.html): \( \sin \theta = \cos(90° - \theta) \).
\( \sin 47° = \cos(90°-47°) = \cos 43° \)
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, \( 1	ext{approximately} 0.7314 \). 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 × \( \sin 47° = 10 × 0.7314 = 7.314 \) 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 — \( \sin 47° = \cos 43° \).

### Mistake 2: Hunting for an exact surd
**Where it slips in:** assuming every angle has a clean value like \( \sin 45°=\frac{\sqrt{2}}{2} \).
**Don't do this:** trying to write \( \sin 47° \) as a simple radical.

### Mistake 3: Forgetting the calculator's angle mode
**Where it slips in:** the calculator was left in radian mode.
**Don't do this:** reporting \( \sin(47) = 0.1236 \) as \( \sin 47° \).

## 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 approximately 0.7314.
- \( \sin 47° \) sits just 0.0243 above \( \sin 45° = 0.7071 \).

## Frequently Asked Questions
- What is sin 47 degrees?
Approximately 0.7314. It sits just above \( \sin 45° = 0.7071 \).  
- Is sin 47 degrees an exact value?
No. 47° is not a special angle, so \( \sin 47° \) 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, \( \sin 47°=\cos 43°=0.7314 \).  
- What is sin 47 degrees in radians?
Approximately \( \frac{47\pi}{180} \), but the sine value is unchanged at approximately 0.7314.  
- Do I need to memorise sin 47 degrees?
No. Non-special angles like 47° are not memorisation targets — you find them with a calculator, a cofunction, or a trigonometric table.