diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index 5c052df1ff48e..b75886b8d99fb 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -1,6 +1,6 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
-import Base: copy, adjoint, getindex, show, transpose, one, zero, inv,
+import Base: copy, adjoint, getindex, show, transpose, one, zero, inv, float,
              hcat, vcat, hvcat, ^
 
 """
@@ -124,6 +124,8 @@ conj(J::UniformScaling) = UniformScaling(conj(J.λ))
 real(J::UniformScaling) = UniformScaling(real(J.λ))
 imag(J::UniformScaling) = UniformScaling(imag(J.λ))
 
+float(J::UniformScaling) = UniformScaling(float(J.λ))
+
 transpose(J::UniformScaling) = J
 adjoint(J::UniformScaling) = UniformScaling(conj(J.λ))
 
@@ -159,7 +161,7 @@ isposdef(J::UniformScaling) = isposdef(J.λ)
 (-)(A::AbstractMatrix, J::UniformScaling)   = A + (-J)
 
 # matrix functions
-for f in ( :exp,   :log,
+for f in ( :exp,   :log, :cis,
            :expm1, :log1p,
            :sqrt,  :cbrt,
            :sin,   :cos,   :tan,
@@ -172,6 +174,9 @@ for f in ( :exp,   :log,
            :acsch, :asech, :acoth )
     @eval Base.$f(J::UniformScaling) = UniformScaling($f(J.λ))
 end
+for f in (:sincos, :sincosd)
+    @eval Base.$f(J::UniformScaling) = map(UniformScaling, $f(J.λ))
+end
 
 # Unit{Lower/Upper}Triangular matrices become {Lower/Upper}Triangular under
 # addition with a UniformScaling
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 6719714049b1e..92547e8648d8a 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -24,6 +24,7 @@ Random.seed!(1234543)
     @test -one(UniformScaling(2)) == UniformScaling(-1)
     @test opnorm(UniformScaling(1+im)) ≈ sqrt(2)
     @test convert(UniformScaling{Float64}, 2I) === 2.0I
+    @test float(2I) === 2.0*I
 end
 
 @testset "getindex" begin
@@ -67,7 +68,7 @@ end
 
     # on complex plane
     J = UniformScaling(randn(ComplexF64))
-    for f in ( exp,   log,
+    for f in ( exp,   log, cis,
                sqrt,
                sin,   cos,   tan,
                asin,  acos,  atan,
@@ -80,6 +81,10 @@ end
         @test f(J) ≈ f(M(J))
     end
 
+    for f in (sincos, sincosd)
+        @test all(splat(≈), zip(f(J), f(M(J))))
+    end
+
     # on real axis
     for (λ, fs) in (
         # functions defined for x ∈ ℝ