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3 years ago

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Corresponding angels are what

1 answer:

Ratling [72]3 years ago

5 0

Answer:

It's when two Angels , on the same side of the transversal, that occupy corresponding positions, one interior and one exterior.

Step-by-step explanation:

<2 and <6 are corresponding Angels

<1 and <5 are corresponding Angels

<3 and <7 are corresponding Angels

<4 and <8 are corresponding Angels

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Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

A recipe calls for 3 cups of sugar for every 4 cups of flour, resulting in ___ cup of sugar for every cup of flour?

kati45 [8]

Answer:

12 cups of sugar

Step-by-step explanation:

i hope it right

3 0

3 years ago

What is the volume?<br> Volume of pi form ?<br><br> 18=height<br> 10=radius

UNO [17]

Answer:

5652

Step-by-step explanation:

Hi there! Let's solve this problem together.

Formula for finding volume in pi: V = pi × radius squared × height

Our height is 18, and our radius is 10. Now, let's calculate.

3.14 x 10 squared (100) = 314.

314 multiplied by 18 is 5,652.

The answer is 5652. I hope this helps you!

3 0

3 years ago

Ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack what is the total amount cloth ,in yards ryan use to make all

Virty [35]

One backpack = 3/4
6 backpacks = 3/4 x 6 = 18/4 = 4.5 yards

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3 years ago

At 6:00 a.m. there were 68 geese in the pond. At 7:30 a.m. There were 50 geese in

Nesterboy [21]

12 geese left per hour. At 7:30 am there were 18 less geese than there were at 6:00 am. Since there was 1.5 hours between each time, and we know that 2/3 of 1.5 hours is 1 hour, we can solve using this equation:

2/3 * 18 = 12.

4 0

3 years ago