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2 years ago

13

Help please!!!!!!!!!!!!!!!!!! marking brainliest for correct answer!!!!!!!!!!!

1 answer:

densk [106]2 years ago

3 0

Step-by-step explanation:

angle 2 = 49

angle 1 = 131

angle 3 = 112

<em>plz </em><em>mark</em><em> my</em><em> answer</em><em> as</em><em> brainlist</em><em>.</em><em>h</em><em>o</em><em>p</em><em>e</em><em> </em><em>this </em><em>will</em><em> be</em><em> helpful</em><em> to</em><em> you</em><em> ☺️</em><em>.</em>

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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

The side lenghts of a triangle are 14,15, and x units

iragen [17]

9514 1404 393

Answer:

1 < x < 29

Step-by-step explanation:

The triangle inequality requires the sum of the two shortest sides exceed the longest side.

<u>When x and 14 are the shortest</u>:

x + 14 > 15

x > 1

<u>When 14 and 15 are the shortest</u>:

14 +15 > x

29 > x

Then the requirement for the length of x is ...

1 < x < 29

_____

<em>Additional comment</em>

The length of the third side of a triangle can be between the difference and sum of the two given sides.

3 0

2 years ago

4. Find the length of Y<br> Find the missing angle marked "e"<br> 11.3<br> 129%<br> 5.91

Allushta [10]

Answer:

b 129%

Step-by-step explanation:

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3 years ago

Can someone help me find the area to this pentagon plz?

natulia [17]

Answer:

3

Step-by-step explanation:

7 0

3 years ago

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If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is given by y = 42t − 16t2. Fi

Andru [333]

$\bf y=42t-16t^2\implies \left. \cfrac{dy}{dt}=42-32t \right|_{t=1}\implies 42-32\implies 10$

8 0

3 years ago