Trigonometry Examples

$\cos (- \frac{3}{5}) \cos (\frac{3}{5}) + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 1

Since $\cos (- \frac{3}{5})$ is an even function, rewrite $\cos (- \frac{3}{5})$ as $\cos (\frac{3}{5})$ .

$\cos (\frac{3}{5}) \cos (\frac{3}{5}) + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 2

Multiply $\cos (\frac{3}{5}) \cos (\frac{3}{5})$ .

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Step 2.1

Raise $\cos (\frac{3}{5})$ to the power of $1$ .

$\cos^{1} (\frac{3}{5}) \cos (\frac{3}{5}) + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 2.2

Raise $\cos (\frac{3}{5})$ to the power of $1$ .

$\cos^{1} (\frac{3}{5}) \cos^{1} (\frac{3}{5}) + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 2.3

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

${\cos (\frac{3}{5})}^{1 + 1} + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 2.4

Add $1$ and $1$ .

$\cos^{2} (\frac{3}{5}) + \cos (\frac{4}{5}) \cos (\frac{4}{5})$

Step 3

Multiply $\cos (\frac{4}{5}) \cos (\frac{4}{5})$ .

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Step 3.1

Raise $\cos (\frac{4}{5})$ to the power of $1$ .

$\cos^{2} (\frac{3}{5}) + \cos^{1} (\frac{4}{5}) \cos (\frac{4}{5})$

Step 3.2

Raise $\cos (\frac{4}{5})$ to the power of $1$ .

$\cos^{2} (\frac{3}{5}) + \cos^{1} (\frac{4}{5}) \cos^{1} (\frac{4}{5})$

Step 3.3

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

$\cos^{2} (\frac{3}{5}) + {\cos (\frac{4}{5})}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$\cos^{2} (\frac{3}{5}) + \cos^{2} (\frac{4}{5})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\cos^{2} (\frac{3}{5}) + \cos^{2} (\frac{4}{5})$

Decimal Form:

$1.16657911 \dots$