Question

How do you express trigonometric expressions in simplest form?

Answer 1

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`