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vagabundo [1.1K]
3 years ago
12

I would really appreciate help with the following, along with work shown so I can understand how these were solved.

Mathematics
1 answer:
Alja [10]3 years ago
6 0

First, you have to know the double angle formula:

sin 2A  =  2 sin A cos A

cos 2A  =  cos² A − sin² A  =  2 cos² A − 1  =  1 − 2 sin² A

tan 2A<span> = 2 tan </span>A<span> / (1 − tan² </span>A)


Next, find the other leg: 17^2-15^=64, √64 is 8, so the unknown leg length is 8.

sinα=15/17, cosα=8/17, tanα=15/8

sinβ=8/17, cosβ15/17, tanβ=8/15

Plug these values in the above formula, you'll have your answers.


For the half angles, know the half-angle formula:

sin(B/2) = ± √<span>(1 − cos B)/2</span>

cos(B/2) = ± √<span>(1 + cos B)/2</span>

tan(B/2)  =  (1 − cos B) / sin B<span>  =  sin </span>B<span> / (1 + cos </span>B)

refer to this website for details:

<span>https://brownmath.com/twt/double.htm
</span>


For the power reduction formula, please search for it. I tried to copy and paste here, but it wouldn't paste. 

for number 4, factor the quadratic equation into (cscx-8)(cscx+1)=0

cscx=8 or cscx=-1

You may not have the csc button on your calculator. Recall that csc is 1/sin, so sinx=1/8 or sinx=-1, so x is either 7.18 or 270 degrees



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If 3a-2b= 8 and a+3b=7 what is the value of 4a+b?
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a+3b=7\\a=7-3b

Step 2: Substitute the value you just found for this variable in the other equation.

3a-2b=8\\3(7-3b)-2b=8\\21-9b-2b=8\\21-11b=8\\21=8+11b\\13=11b\\\frac{13}{11}=b\\ b=1\frac{2}{11}

Step 3: Use your new value for the second variable to find the first.

a+3b=7\\a+3(1\frac{2}{11})=7\\a+3\frac{6}{11}=7\\\\a=3\frac{5}{11}

Now that we know the values for a and b we can find the value of 4a+b.

4a+b\\4(3\frac{5}{11})+1\frac{2}{11}\\12+\frac{20}{11}+1\frac{2}{11}\\\\12+1\frac{9}{11}+1\frac{2}{11}\\\\\boxed{15}
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