How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{5 π}{3})$ $sin(pi/ 8 ) * cos(( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{5 π}{3})$ $sin(pi/ 8 ) * cos(( ( 5 pi) / 3 )$ without using products of trigonometric functions?

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Answer 1 · 2017-12-09T07:33:46

The answer is $= \frac{1}{2} (sin (\frac{1}{3} π) - sin (\frac{5}{24} π))$ $=1/2(sin(1/3pi)-sin(5/24pi))$

Explanation:

Apply the formula

$sin a cos b = \frac{1}{2} (sin (a + b) + sin (a - b))$ $sinacosb=1/2(sin(a+b)+sin(a-b))$

You can easily prove this formula by using $sin (a + b)$ $sin(a+b)$ and $sin (a - b)$ $sin(a-b)$

Here,

$a = \frac{1}{8} π$ $a=1/8pi$ and $b = \frac{5}{3} π$ $b=5/3pi$

Therefore,

$sin (\frac{1}{8} π) cos (\frac{5}{3} π) = \frac{1}{2} (sin (\frac{1}{8} π + \frac{5}{3} π) + sin (\frac{1}{8} π - \frac{5}{3} π))$ $sin(1/8pi)cos(5/3pi)=1/2(sin(1/8pi+5/3pi)+sin(1/8pi-5/3pi))$

$= \frac{1}{2} (sin (\frac{43}{24} π) + sin (- \frac{37}{24} π))$ $=1/2(sin(43/24pi)+sin(-37/24pi))$

$= \frac{1}{2} (sin (- \frac{5}{24} π) + sin (\frac{8}{24} π))$ $=1/2(sin(-5/24pi)+sin(8/24pi))$

$= \frac{1}{2} (sin (\frac{1}{3} π) - sin (\frac{5}{24} π))$ $=1/2(sin(1/3pi)-sin(5/24pi))$

Answer 2 · 2017-12-09T07:34:57

Simply calculate the given terms.
$= 0.00682$ $= 0.00682$

Explanation:

You "using products of trig functions" statement is not clear. I took it to mean revising the expression to form a single trigonometric identity.

Thus, to avoid that, I simply evaluated the expression by each term.
$sin(π/8) xx cos(5π/3) = 0.00685 xx 0.9958 = 0.00682$

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How do you express $sin (\frac{π}{8}) \cdot cos ((\frac{5 π}{3})$ $sin(pi/ 8 ) * cos(( ( 5 pi) / 3 )$ without using products of trigonometric functions?

2 Answers

Explanation:

Explanation:

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