diff --git a/base/math.jl b/base/math.jl
index 9a5e5377cf6132..704557adc5f2e9 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -1318,6 +1318,9 @@ for f in (:sin, :cos, :tan, :asin, :atan, :acos,
     end
     @eval $(f)(::Missing) = missing
 end
+atan(::Missing, ::Missing) = missing
+atan(::Number, ::Missing) = missing
+atan(::Missing, ::Number) = missing
 
 exp2(x::AbstractFloat) = 2^x
 exp10(x::AbstractFloat) = 10^x
diff --git a/test/missing.jl b/test/missing.jl
index 0be8cb8ec9be41..c20dc21f188d34 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -109,6 +109,19 @@ end
     end
 end
 
+@testset "two-argument functions" begin
+    two_argument_functions = [atan]
+
+    # All two-argument functions return missing when operating on two missing's
+    # All two-argument functions return missing when operating on a scalar and an missing
+    # All two-argument functions return missing when operating on an missing and a scalar
+    for f in two_argument_functions
+        @test ismissing(f(missing, missing))
+        @test ismissing(f(1, missing))
+        @test ismissing(f(missing, 1))
+    end
+end
+
 @testset "bit operators" begin
     bit_operators = [&, |, ⊻]