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3 years ago

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3 * 9 + (6 + 5 – 3) – 12 : 4 =

1 answer:

xeze [42]3 years ago

7 0

Answer:

23,4

Step-by-step explanation:

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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

Which graph represents y=x-5?

elena-s [515]

Can uu show the rest of the graph??????

3 0

2 years ago

Find the area of each circle round to the nearest tenth use 20 yard

stiv31 [10]

Answer:

Step-by-step explanation:

3 0

2 years ago

The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes? Solve this problem

densk [106]

So, The Crayola Crayon company can make 2400 crayons in 4 minutes. In other words, every 4 minutes they can make 2400 crayons, right? So, in 15 minutes how many would they have made? Well, what we do is we divide 15 by 4 which is 3.75. Then we multiply the result, 3.75, by 2400. 3.75 * 9000. So, in 15 minutes, Crayola would have made 900 crayons!

4/2400 = 15/x

Step 1: Cross Multiply

4/2400 = 15/x

4 * x = (15) * (2400)

4x = 36000

Step 2: Divide both sides by 2

4x/4 = 36000/2

x = 9000

The answer is, 9000!!! :D

4 0

3 years ago

What is the volume of this cone?

Romashka-Z-Leto [24]

Answer:

3537.73 cubic in

Step-by-step explanation:

Given,

Diameter of the cone = 26 in

Radius of the cone = 26in ÷ 2 = 13 in

Height of the cone = 20 in

Therefore, volume of the cone

$= \frac{1}{3} \pi {r}^{2} h$

$= \frac{1}{3} \times 3.14 \times 13 \times 13 \times 20$

$= 3,537.7333333333 \: {in}^{3}$

<u>Approx. 3537 . 73 cubic in (Ans)</u>

8 0

3 years ago

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