diff --git a/base/math.jl b/base/math.jl
index 71bd4949498b5..0f917dce7c99c 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -1571,7 +1571,7 @@ sincos(a::Float16) = Float16.(sincos(Float32(a)))
 for f in (:sin, :cos, :tan, :asin, :atan, :acos,
           :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
           :exp, :exp2, :exp10, :expm1, :log, :log2, :log10, :log1p,
-          :exponent, :sqrt, :cbrt)
+          :exponent, :sqrt, :cbrt, :sinpi, :cospi, :sincospi, :tanpi)
     @eval function ($f)(x::Real)
         xf = float(x)
         x === xf && throw(MethodError($f, (x,)))
diff --git a/base/special/trig.jl b/base/special/trig.jl
index 6463560caa3e5..50d3d69585217 100644
--- a/base/special/trig.jl
+++ b/base/special/trig.jl
@@ -789,16 +789,14 @@ Compute ``\\sin(\\pi x)`` more accurately than `sin(pi*x)`, especially for large
 
 See also [`sind`](@ref), [`cospi`](@ref), [`sincospi`](@ref).
 """
-function sinpi(_x::T) where T<:Union{IEEEFloat, Rational}
+function sinpi(_x::T) where T<:IEEEFloat
     x = abs(_x)
     if !isfinite(x)
         isnan(x) && return x
         throw(DomainError(x, "`x` cannot be infinite."))
     end
     # For large x, answers are all 1 or zero.
-    if T <: AbstractFloat
-        x >= maxintfloat(T) && return copysign(zero(T), _x)
-    end
+    x >= maxintfloat(T) && return copysign(zero(T), _x)
 
     # reduce to interval [0, 0.5]
     n = round(2*x)
@@ -820,16 +818,14 @@ end
 
 Compute ``\\cos(\\pi x)`` more accurately than `cos(pi*x)`, especially for large `x`.
 """
-function cospi(x::T) where T<:Union{IEEEFloat, Rational}
+function cospi(x::T) where T<:IEEEFloat
     x = abs(x)
     if !isfinite(x)
         isnan(x) && return x
         throw(DomainError(x, "`x` cannot be infinite."))
     end
     # For large x, answers are all 1 or zero.
-    if T <: AbstractFloat
-        x >= maxintfloat(T) && return one(T)
-    end
+    x >= maxintfloat(T) && return one(T)
 
     # reduce to interval [0, 0.5]
     n = round(2*x)
@@ -856,16 +852,14 @@ where `x` is in radians), returning a tuple `(sine, cosine)`.
 
 See also: [`cispi`](@ref), [`sincosd`](@ref), [`sinpi`](@ref).
 """
-function sincospi(_x::T) where T<:Union{IEEEFloat, Rational}
+function sincospi(_x::T) where T<:IEEEFloat
     x = abs(_x)
     if !isfinite(x)
         isnan(x) && return x, x
         throw(DomainError(x, "`x` cannot be infinite."))
     end
     # For large x, answers are all 1 or zero.
-    if T <: AbstractFloat
-        x >= maxintfloat(T) && return (copysign(zero(T), _x), one(T))
-    end
+    x >= maxintfloat(T) && return (copysign(zero(T), _x), one(T))
 
     # reduce to interval [0, 0.5]
     n = round(2*x)
@@ -895,7 +889,7 @@ Compute ``\\tan(\\pi x)`` more accurately than `tan(pi*x)`, especially for large
 
 See also [`tand`](@ref), [`sinpi`](@ref), [`cospi`](@ref), [`sincospi`](@ref).
 """
-function tanpi(_x::T) where T<:Union{IEEEFloat, Rational}
+function tanpi(_x::T) where T<:IEEEFloat
     # This is modified from sincospi.
     # Would it be faster or more accurate to make a tanpi_kernel?
     x = abs(_x)
@@ -905,9 +899,7 @@ function tanpi(_x::T) where T<:Union{IEEEFloat, Rational}
     end
     # For large x, answers are all zero.
     # All integer values for floats larger than maxintfloat are even.
-    if T <: AbstractFloat
-        x >= maxintfloat(T) && return copysign(zero(T), _x)
-    end
+    x >= maxintfloat(T) && return copysign(zero(T), _x)
 
     # reduce to interval [0, 0.5]
     n = round(2*x)
@@ -932,10 +924,10 @@ cospi(x::Integer) = isodd(x) ? -one(float(x)) : one(float(x))
 tanpi(x::Integer) = x >= 0 ? (isodd(x) ? -zero(float(x)) : zero(float(x))) :
                              (isodd(x) ? zero(float(x)) : -zero(float(x)))
 sincospi(x::Integer) = (sinpi(x), cospi(x))
-sinpi(x::Real) = sin(pi*x)
-cospi(x::Real) = cos(pi*x)
-sincospi(x::Real) = sincos(pi*x)
-tanpi(x::Real) = tan(pi*x)
+sinpi(x::AbstractFloat) = sin(pi*x)
+cospi(x::AbstractFloat) = cos(pi*x)
+sincospi(x::AbstractFloat) = sincos(pi*x)
+tanpi(x::AbstractFloat) = tan(pi*x)
 tanpi(x::Complex) = sinpi(x) / cospi(x) # Is there a better way to do this?
 
 function sinpi(z::Complex{T}) where T
diff --git a/test/math.jl b/test/math.jl
index 19d9f7893a496..8e6afba0acfce 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -1558,3 +1558,9 @@ for T in (Float16, Float32, Float64)
     @test Core.Compiler.is_foldable(Base.infer_effects(^, (T,Int)))
     @test Core.Compiler.is_foldable(Base.infer_effects(^, (T,T)))
 end
+
+@testset "BigInt Rationals with special funcs" begin
+    @test sinpi(big(1//1)) == big(0.0)
+    @test tanpi(big(1//1)) == big(0.0)
+    @test cospi(big(1//1)) == big(-1.0)
+end