How do you express trigonometric expressions in simplest form?

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How do you express trigonometric expressions in simplest form?

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Answer 1 · 2015-04-12T14:20:35

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

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

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How do you express trigonometric expressions in simplest form?

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