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vesna_86 [32]
2 years ago
8

Please help me with those questions

Mathematics
1 answer:
KengaRu [80]2 years ago
6 0
I’ve attached my work...
Hope it helps!
If you have any questions, comment!
Have a nice day or night:)

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Find the exact value by using a half-angle identity. sin(5pi/12)
anzhelika [568]

Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>

Explanation:

Call tan ((5pi/12) = t. 
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>

<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>

<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>

Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>

5 0
3 years ago
Which property justifies the following equation?
Leviafan [203]
1. . D . Identity , when you odd both properties it will always to be true on both sides
5 0
3 years ago
Sharon borrowed $750 at 12% for one year. She paid a $20 processing fee. How much will she pay in interest?
Hunter-Best [27]

Answer:

$90

Step-by-step explanation:

The principal amount in the loan taken by Sharon is $750 . Note hat the $20 processing fee is a one time cost and is not included in the interest calculation.

Annual Rate of interest offered to Sharon is 12%

Time interval for the loan transaction is 1 year.

So the interest for 1 year is given by \[Principal * Rate * Year /100\]

\[750 * 12 * 1 /100\] = $90

So, Sharon will have to pay $90 as interest for the loan amount $750 borrowed for one year at the rate 12%.

8 0
3 years ago
Triangle ABC is rotated to create the image A'B'C
Alborosie

Is there more to this?


3 0
3 years ago
Read 2 more answers
FOR A BRAINLIST PLS HURRY
insens350 [35]

Answer:

y = x

Step-by-step explanation:

line has a slope 1 and passes through the origin . So the equation is y = x

8 0
2 years ago
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