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