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insens350 [35]
3 years ago
8

Using sum or difference formulas, find the exact value of sin(165∘)

Mathematics
1 answer:
Nikitich [7]3 years ago
6 0
\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})\\\\
-------------------------------\\\\

\bf sin(165^o)\implies sin(120^o+45^o)
\\\\\\
sin(120^o)cos(45^o)~+~cos(120^o)sin(45^o)\implies \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}~+~\cfrac{-1}{2}\cdot \cfrac{\sqrt{2}}{2}
\\\\\\
\cfrac{\sqrt{6}}{4}~-~\cfrac{\sqrt{2}}{4}\implies \cfrac{\sqrt{6}-\sqrt{2}}{4}
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OLga [1]

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Step-by-step explanation:

i =  \sqrt{ - 1}  \\ (3 - 4i)( - 6 + i) \\  = (3 - 4 \sqrt{ - 1} )( - 6 +  \sqrt{ - 1} ) \\  = 3( - 6 +  \sqrt{ - 1)}  - 4 \sqrt{ - 1} ( - 6 +  \sqrt{ - 1} ) \\  =  - 18 + 3 \sqrt{ - 1}  + 24 \sqrt{ - 1}  - 4 \\  =  - 22 + 27 \sqrt{ - 1} \\ putting \:  \:  \:  \sqrt{ - 1 }  = i \\  =  - 22 + 27i

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8 0
2 years ago
The product of a number and -8 gives eight times the sum of that number and 36. Find that number
Viefleur [7K]

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-18

Step-by-step explanation:

Let x be our number. First we have to write our equation.

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The result is eight times the sum of x and 36. This is represented as 8(x + 36). We add x and 36 first because 8 has been multiplied by the sum of those two numbers.

So our equation is:

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We can now solve for x. First, expand the bracket.

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Next, subtract 8x from both sides. This will give us only one term containing x, which will make it easier to solve.

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3 0
3 years ago
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