Sage has several methods that are used primarily when an expression involves trigonometric functions. Let's try them out.
var('x, y')
f(x, y) = sin(x) * cos(x)^3 + sin(y)^2
print("f(x, y)")
f.show()
g(x, y) = f.reduce_trig() # also trig_reduce
print("After trig_reduce:")
g.show()
print("After expanding:")
show(g.expand_trig()) # also trig_expand
print("Simplify to get original expression:")
show(g.expand_trig().trig_simplify()) # also simplify_trigThe output is shown in the following screenshot:
We demonstrated some useful methods that are specifically designed to manipulate expressions that involve trigonometric functions. expand_trig and reduce_trig (or trig_expand and trig_reduce) are complementary methods that have a similar function to those used in the previous example. We also introduced the method called trig_simplify (or simplify_trig), which attempts to represent an expression in the most...