Precalculus Examples

$\sin (\frac{π}{5}) \cos (\frac{π}{11}) + \cos (\frac{π}{5}) \sin (\frac{π}{11})$

Step 1

The result can be shown in multiple forms.

Exact Form:

$\sin (\frac{π}{5}) \cos (\frac{π}{11}) + \cos (\frac{π}{5}) \sin (\frac{π}{11})$

Decimal Form:

$0.79190224 \dots$

Step 2

Simplify $E x a c t (F o r m) : \sin (\frac{π}{5}) \cos (\frac{π}{11}) + \cos (\frac{π}{5}) \sin (\frac{π}{11}) D e c i m a l (F o r m) : 0.79190224 \dots$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Evaluate $\sin (\frac{π}{5})$ .

$E x a c t F o r m :$

$0.58778525 \cos (\frac{π}{11}) + \cos (\frac{π}{5}) \sin (\frac{π}{11})$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.1.2

Evaluate $\cos (\frac{π}{11})$ .

$E x a c t F o r m :$

$0.58778525 \cdot 0.95949297 + \cos (\frac{π}{5}) \sin (\frac{π}{11})$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.1.3

Multiply $0.58778525$ by $0.95949297$ .

$E x a c t F o r m :$

$0.56397581 + \cos (\frac{π}{5}) \sin (\frac{π}{11})$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.1.4

Evaluate $\cos (\frac{π}{5})$ .

$E x a c t F o r m :$

$0.56397581 + 0.80901699 \sin (\frac{π}{11})$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.1.5

Evaluate $\sin (\frac{π}{11})$ .

$E x a c t F o r m :$

$0.56397581 + 0.80901699 \cdot 0.28173255$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.1.6

Multiply $0.80901699$ by $0.28173255$ .

$E x a c t F o r m :$

$0.56397581 + 0.22792642$

$D e c i m a l (F o r m) :$

$0.79190224$

$E x a c t F o r m :$

$0.56397581 + 0.22792642$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.2

Add $0.56397581$ and $0.22792642$ .

$E x a c t F o r m :$

$0.79190224$

$D e c i m a l (F o r m) :$

$0.79190224$

Step 2.3

Multiply $m$ by $m$ by adding the exponents.

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Step 2.3.1

Move $m$ .

$E x a c t F o r m :$

$0.79190224$

$D e c i (m \cdot m) a l (F o r) :$

$0.79190224$

Step 2.3.2

Multiply $m$ by $m$ .

$E x a c t F o r m :$

$0.79190224$

$D e c i m^{2} a l (F o r) :$

$0.79190224$

$E x a c t F o r m :$

$0.79190224$

$D e c i m^{2} a l F o r :$

$0.79190224$

$E x a c t F o r m :$

$0.79190224$

$D e c i m^{2} a l F o r :$

$0.79190224$

Step 3

Since there are no common prime factors, the only common factor for $E x a c t (F o r m) : \sin (\frac{π}{5}) \cos (\frac{π}{11}) + \cos (\frac{π}{5}) \sin (\frac{π}{11}) D e c i m a l (F o r m) : 0.79190224 \dots$ is $1$ .

$1$