define sin/cos on Dual to use sincos (#561)

Author: KristofferC

src/dual.jl

@@ -393,7 +393,7 @@ Base.float(d::Dual) = convert(float(typeof(d)), d)
 ###################################
 
 for (M, f, arity) in DiffRules.diffrules(filter_modules = nothing)
-    if (M, f) in ((:Base, :^), (:NaNMath, :pow), (:Base, :/), (:Base, :+), (:Base, :-))
+    if (M, f) in ((:Base, :^), (:NaNMath, :pow), (:Base, :/), (:Base, :+), (:Base, :-), (:Base, :sin), (:Base, :cos))
         continue  # Skip methods which we define elsewhere.
     elseif !(isdefined(@__MODULE__, M) && isdefined(getfield(@__MODULE__, M), f))
         continue  # Skip rules for methods not defined in the current scope
@@ -622,12 +622,19 @@ end
     Dual{Tz}(muladd(x, y, value(z)), partials(z))      # z_body
 )
 
-# sincos #
+# sin/cos #
 #--------#
+function Base.sin(d::Dual{T}) where T
+    s, c = sincos(value(d))
+    return Dual{T}(s, c * partials(d))
+end
 
-@inline sincos(x) = (sin(x), cos(x))
+function Base.cos(d::Dual{T}) where T
+    s, c = sincos(value(d))
+    return Dual{T}(c, -s * partials(d))
+end
 
-@inline function sincos(d::Dual{T}) where T
+@inline function Base.sincos(d::Dual{T}) where T
     sd, cd = sincos(value(d))
     return (Dual{T}(sd, cd * partials(d)), Dual{T}(cd, -sd * partials(d)))
 end