Trigonometry Examples

${(r \cos (1) + 5)}^{2}$

Step 1

Rewrite ${(r \cos (1) + 5)}^{2}$ as $(r \cos (1) + 5) (r \cos (1) + 5)$ .

$(r \cos (1) + 5) (r \cos (1) + 5)$

Step 2

Expand $(r \cos (1) + 5) (r \cos (1) + 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$r \cos (1) (r \cos (1) + 5) + 5 (r \cos (1) + 5)$

Step 2.2

Apply the distributive property.

$r \cos (1) (r \cos (1)) + r \cos (1) \cdot 5 + 5 (r \cos (1) + 5)$

Step 2.3

Apply the distributive property.

$r \cos (1) (r \cos (1)) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $r$ by $r$ by adding the exponents.

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Step 3.1.1.1

Move $r$ .

$r \cdot r \cos (1) \cos (1) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.1.2

Multiply $r$ by $r$ .

$r^{2} \cos (1) \cos (1) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.2

Multiply $r^{2} \cos (1) \cos (1)$ .

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Step 3.1.2.1

Raise $\cos (1)$ to the power of $1$ .

$r^{2} (\cos^{1} (1) \cos (1)) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.2.2

Raise $\cos (1)$ to the power of $1$ .

$r^{2} (\cos^{1} (1) \cos^{1} (1)) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$r^{2} {\cos (1)}^{1 + 1} + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.2.4

Add $1$ and $1$ .

$r^{2} \cos^{2} (1) + r \cos (1) \cdot 5 + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.3

Move $5$ to the left of $r \cos (1)$ .

$r^{2} \cos^{2} (1) + 5 \cdot (r \cos (1)) + 5 (r \cos (1)) + 5 \cdot 5$

Step 3.1.4

Multiply $5$ by $5$ .

$r^{2} \cos^{2} (1) + 5 r \cos (1) + 5 r \cos (1) + 25$

Step 3.2

Add $5 r \cos (1)$ and $5 r \cos (1)$ .

$r^{2} \cos^{2} (1) + 10 r \cos (1) + 25$