How do you express trigonometric expressions in simplest form?

1 Answer
Apr 12, 2015

Examples of trig expressions: # f(x) = sin 2x + cos x; #
#f(x) = sin x + sin 2x + sin 3x#
Examples of trig equations: # f(x) = sin 2x + cos x = 0#
# f(x) = sin x + sin 2x + sin 3x = 0#
Examples of trig inequalities #f(x) = sin 2x + cos x > 0#
# f(x) = sin x + sin 2x + sin 3x < 0#

Use trig Transformation Identities to transform these above trig expressions into trig basic expressions, or expressions in simplest form.
Example: Transform #f(x) = sin 2x + cos x#. Use Identity #(sin 2a = 2 sin a*cos a)# to transform #f(x).#
#f(x) = 2*sin x*cos x + cos x = cos x*(2sin x + 1)#
This is f(x) expressed in simplest form.
Trig equation in simplest form: #f(x) = cos x*(sin 2x + 1) = 0#
Trig inequality in simplest form: #f(x) = cos x*(2sinx + 1) > 0#