diff --git a/PreciseNumber.Test/PreciseNumberTrigonometryTests.cs b/PreciseNumber.Test/PreciseNumberTrigonometryTests.cs
index ecc8df1..e2c0c6d 100644
--- a/PreciseNumber.Test/PreciseNumberTrigonometryTests.cs
+++ b/PreciseNumber.Test/PreciseNumberTrigonometryTests.cs
@@ -151,6 +151,37 @@ public void TestSinDeliversEveryDigitUpToTheReductionCeiling()
 		AssertAgreesTo(Parse(SinOneMillionDigits), sine, 120, "Sin at the reduction ceiling did not match its wide reference");
 	}
 
+	[TestMethod]
+	public void TestTanDeliversEveryDigitUpToTheReductionCeiling()
+	{
+		// Tan widens by its guard digits before computing sin and cos. Those are margin, so they must
+		// not be counted against the ceiling: Tan has to reach the same precision Sin and Cos do.
+		int ceiling = PreciseNumber.ConstantPrecision - 7;
+		PreciseNumber million = Parse("1000000");
+		PreciseNumber tangent = PreciseNumber.Tan(million, ceiling);
+		(PreciseNumber sin, PreciseNumber cos) = PreciseNumber.SinCos(million, ceiling);
+
+		Assert.AreEqual(ceiling, tangent.SignificantDigits);
+		AssertAgreesTo(PreciseNumber.Divide(sin, cos, ceiling), tangent, ceiling - 2, "Tan at the reduction ceiling was not sin/cos");
+
+		// One digit past the ceiling is still refused, as it is for Sin.
+		Assert.ThrowsExactly<ArgumentOutOfRangeException>(() => PreciseNumber.Tan(million, ceiling + 1));
+	}
+
+	[TestMethod]
+	public void TestTanAcceptsThePrecisionsSinAndCosAccept()
+	{
+		// The issue's reproduction: each of these is within the ceiling for Sin and Cos, and Tan
+		// refused them because its guard digits were checked as if they were part of the answer.
+		PreciseNumber one = PreciseNumber.One;
+		PreciseNumber tangent = PreciseNumber.Tan(one, 145);
+
+		Assert.AreEqual(145, tangent.SignificantDigits);
+		StringAssert.StartsWith(Digits(tangent), Tan1Digits, StringComparison.Ordinal, "Tan(1, 145) is wrong");
+		Assert.AreEqual(145, PreciseNumber.Tan(Parse("0.3"), 145).SignificantDigits);
+		Assert.AreEqual(PreciseNumber.ConstantPrecision, PreciseNumber.Tan(Parse("0.3"), PreciseNumber.ConstantPrecision).SignificantDigits);
+	}
+
 	[TestMethod]
 	public void TestSinRefusesAnArgumentTooLargeToReduceAtAll()
 	{
diff --git a/PreciseNumber/PreciseNumber.Trigonometry.cs b/PreciseNumber/PreciseNumber.Trigonometry.cs
index 3c6e87a..17f2e03 100644
--- a/PreciseNumber/PreciseNumber.Trigonometry.cs
+++ b/PreciseNumber/PreciseNumber.Trigonometry.cs
@@ -183,7 +183,25 @@ public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x) =>
 	public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x, int significantDigits)
 	{
 		RequireSignificantDigits(significantDigits);
+		RequireReducibleArgument(significantDigits, IntegerDigitCount(x));
+		return SinCosCore(x, significantDigits);
+	}
 
+	/// <summary>
+	/// Computes the sine and cosine of an angle in radians without checking the precision against
+	/// the reduction ceiling.
+	/// </summary>
+	/// <param name="x">The angle, in radians.</param>
+	/// <param name="significantDigits">The number of significant digits to produce, at least one.</param>
+	/// <returns>A tuple of the sine and cosine of <paramref name="x"/>.</returns>
+	/// <remarks>
+	/// The body of <see cref="SinCos(PreciseNumber, int)"/>, for a caller that has already checked
+	/// the digits it will report and wants these computed wider as guard margin. Margin is allowed to
+	/// be unavailable (see <see cref="RequireReducibleArgument(int, int)"/>), so checking the widened
+	/// precision would refuse requests whose every reported digit is correct.
+	/// </remarks>
+	private static (PreciseNumber Sin, PreciseNumber Cos) SinCosCore(PreciseNumber x, int significantDigits)
+	{
 		if (x.Significand.IsZero)
 		{
 			return (Zero, One);
@@ -196,8 +214,6 @@ public static (PreciseNumber Sin, PreciseNumber Cos) SinCos(PreciseNumber x, int
 		int argumentDigits = IntegerDigitCount(x);
 		int reductionDigits = working + argumentDigits + TrigonometricGuardDigits;
 
-		RequireReducibleArgument(significantDigits, argumentDigits);
-
 		PreciseNumber piOverTwo = Divide(PiTo(reductionDigits), Two, reductionDigits);
 		BigInteger quadrant = RoundToNearestInteger(Divide(x, piOverTwo, reductionDigits));
 		PreciseNumber remainder = Subtract(x, Multiply(new(0, quadrant), piOverTwo))
@@ -226,16 +242,23 @@ public static PreciseNumber Tan(PreciseNumber x) =>
 	/// <param name="x">The angle, in radians.</param>
 	/// <param name="significantDigits">The number of significant digits to produce.</param>
 	/// <returns>The tangent of <paramref name="x"/>.</returns>
-	/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="significantDigits"/> is less than one.</exception>
+	/// <exception cref="ArgumentOutOfRangeException">
+	/// Thrown when <paramref name="significantDigits"/> is less than one, or when it and the integer
+	/// digits of <paramref name="x"/> together exceed <see cref="ConstantPrecision"/>, exactly as for
+	/// <see cref="SinCos(PreciseNumber, int)"/>.
+	/// </exception>
 	/// <exception cref="DivideByZeroException">Thrown when the cosine of <paramref name="x"/> is zero.</exception>
 	/// <remarks>
 	/// <c>sin / cos</c> from one reduction and a single division, rather than two independent series.
+	/// The ceiling is checked against the requested digits only; the sine and cosine are then
+	/// computed wider as guard margin, which is not counted against it.
 	/// </remarks>
 	public static PreciseNumber Tan(PreciseNumber x, int significantDigits)
 	{
 		RequireSignificantDigits(significantDigits);
+		RequireReducibleArgument(significantDigits, IntegerDigitCount(x));
 		int working = significantDigits + TrigonometricGuardDigits;
-		(PreciseNumber sin, PreciseNumber cos) = SinCos(x, working);
+		(PreciseNumber sin, PreciseNumber cos) = SinCosCore(x, working);
 		return DivideApproximation(sin, cos, working, significantDigits);
 	}