Trigonometry Examples

$\sin^{2} (x) - 4 \sin (x) + 3$

Step 1

Let $u = \sin (x)$ . Substitute $u$ for all occurrences of $\sin (x)$ .

$u^{2} - 4 u + 3$

Step 2

Factor $u^{2} - 4 u + 3$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 2.2

Write the factored form using these integers.

$(u - 3) (u - 1)$

Step 3

Replace all occurrences of $u$ with $\sin (x)$ .

$(\sin (x) - 3) (\sin (x) - 1)$