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marusya05 [52]
2 years ago
10

Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 < 2pi. Show work please!

Mathematics
1 answer:
yan [13]2 years ago
7 0

Answer:

\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

cos(2\theta)=1-2sin^2(\theta)

so we will make that replacement, getting everything in terms of sin:

sin(\theta)+1=1-2sin^2(\theta)

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

2sin^2(\theta)+sin(\theta)=0

We can factor out the sin(theta), since it's common in both terms:

sin(\theta)(2sin(\theta)+1)=0

Because of the Zero Product Property, either

sin(\theta)=0 or

2sin(\theta)+1=0

Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi.  They are:

\theta=\frac{\pi}{2},\frac{3\pi}{2}

The next equation needs to first be solved for sin(theta):

2sin(\theta)+1=0 so

2sin(\theta)=-1 and

sin(\theta)=-\frac{1}{2}

Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

\theta=\frac{2\pi}{3},\frac{4\pi}{3}

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bonufazy [111]

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Answer:

  a) The new triangle is a reflection of the original across the origin. All angles, segment lengths, and line slopes have been preserved: the transformed triangle is congruent with the original.

  b) The new triangle is a reflection of the original across the origin and a dilation by a factor of 2. Angles have been preserved: the transformed triangle is similar to the original. The transformation is NOT rigid.

Step-by-step explanation:

1. The transformed triangle is blue in the attachment. It is congruent with the original. The transformation is "rigid," a reflection across the origin. All angles and lengths have been preserved, as well as line slopes.

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2. The transformed triangle is orange in the attachment. It is similar to the original, in that angles have been preserved and lengths are proportional. It is a reflection across the origin and a dilation by a factor of 2. Line slopes have also been preserved. A dilation is NOT a "rigid" transformation.

4 0
2 years ago
Whats the value of x
fiasKO [112]

Answer:

x=14

Step-by-step explanation:

you should set up your problem like this:

5x=3x+28

use order of operations aka PEMDAS to solve

you're answer is 14

8 0
2 years ago
Solve the following equation for s P=b+2s
laiz [17]

Answer:

s=P-b/2

Step-by-step explanation:

P-b=2s

P-b/2=s

3 0
2 years ago
Help me please I don't know this
Nutka1998 [239]

Answer:

I'll give you a hint

Step-by-step explanation:

The angles are not supplementary, which means they add up to 180 degrees, they are complementary, which means they add up to 90 degrees

Hope this helps!

3 0
2 years ago
Read 2 more answers
A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide it in half with a fence paral
denis23 [38]

Answer:

  F = 3x +(2.7×10^7)/x

Step-by-step explanation:

The formulas for area and perimeter of a rectangle can be used to find the desired function.

<h3>Area</h3>

The area of the rectangle will be the product of its dimensions:

  A = LW

Using the given values, we have ...

  13.5×10^6 = xy

Solving for y gives ...

  y = (13.5×10^6)/x

<h3>Perimeter</h3>

The perimeter of the rectangle is the sum of the side lengths:

  P = 2(L+W) = 2(x+y)

<h3>Fence length</h3>

The total amount of fence required is the perimeter plus one more section that is x feet long.

  F = 2(x +y) +x = 3x +2y

Substituting for y, we have a function of x:

  F = 3x +(2.7×10^7)/x

__

<em>Additional comment</em>

The length of fence required is minimized for x=3000. The overall size of that fenced area is x=3000 ft by y=4500 ft. Each half is 3000 ft by 2250 ft. Half of the total 18000 ft of fence is used for each of the perpendicular directions: 3x=2y=9000 ft.

4 0
1 year ago
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