diff --git a/base/linalg/diagonal.jl b/base/linalg/diagonal.jl
index 173a2236cf0e9..93533a4b02f64 100644
--- a/base/linalg/diagonal.jl
+++ b/base/linalg/diagonal.jl
@@ -345,9 +345,13 @@ end
 eye(::Type{Diagonal{T}}, n::Int) where {T} = Diagonal(ones(T,n))
 
 # Matrix functions
-exp(D::Diagonal) = Diagonal(exp.(D.diag))
-log(D::Diagonal) = Diagonal(log.(D.diag))
-sqrt(D::Diagonal) = Diagonal(sqrt.(D.diag))
+for f in (:exp, :log, :sqrt,
+          :cos, :sin, :tan, :csc, :sec, :cot,
+          :cosh, :sinh, :tanh, :csch, :sech, :coth,
+          :acos, :asin, :atan, :acsc, :asec, :acot,
+          :acosh, :asinh, :atanh, :acsch, :asech, :acoth)
+    @eval $f(D::Diagonal) = Diagonal($f.(D.diag))
+end
 
 #Linear solver
 function A_ldiv_B!(D::Diagonal, B::StridedVecOrMat)
diff --git a/test/linalg/diagonal.jl b/test/linalg/diagonal.jl
index 3ba9c7c757099..d57807c9eaf6c 100644
--- a/test/linalg/diagonal.jl
+++ b/test/linalg/diagonal.jl
@@ -71,13 +71,15 @@ srand(1)
             @test func(D) ≈ func(DM) atol=n^2*eps(relty)*(1+(elty<:Complex))
         end
         if relty <: BlasFloat
-            for func in (exp,)
+            for func in (exp, sinh, cosh, tanh, sech, csch, coth)
                 @test func(D) ≈ func(DM) atol=n^3*eps(relty)
             end
             @test log(Diagonal(abs.(D.diag))) ≈ log(abs.(DM)) atol=n^3*eps(relty)
         end
         if elty <: BlasComplex
-            for func in (logdet, sqrt)
+            for func in (logdet, sqrt, sin, cos, tan, sec, csc, cot,
+                         asin, acos, atan, asec, acsc, acot,
+                         asinh, acosh, atanh, asech, acsch, acoth)
                 @test func(D) ≈ func(DM) atol=n^2*eps(relty)*2
             end
         end