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agasfer [191]
3 years ago
14

Please Help! This is a trigonometry question.

Mathematics
1 answer:
liraira [26]3 years ago
8 0
\large\begin{array}{l} \textsf{From the picture, we get}\\\\ \mathsf{tan\,\theta=\dfrac{2}{3}}\\\\ \mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{2}{3}}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\qquad\mathsf{(i)} \end{array}


\large\begin{array}{l} \textsf{Square both sides of \mathsf{(i)} above:}\\\\ \mathsf{(3\,sin\,\theta)^2=(2\,cos\,\theta)^2}\\\\ \mathsf{9\,sin^2\,\theta=4\,cos^2\,\theta}\qquad\quad\textsf{(but }\mathsf{cos^2\theta=1-sin^2\,\theta}\textsf{)}\\\\ \mathsf{9\,sin^2\,\theta=4\cdot (1-sin^2\,\theta)}\\\\ \mathsf{9\,sin^2\,\theta=4-4\,sin^2\,\theta}\\\\ \mathsf{9\,sin^2\,\theta+4\,sin^2\,\theta=4} \end{array}

\large\begin{array}{l} \mathsf{13\,sin^2\,\theta=4}\\\\ \mathsf{sin^2\,\theta=\dfrac{4}{13}}\\\\ \mathsf{sin\,\theta=\sqrt{\dfrac{4}{13}}}\\\\ \textsf{(we must take the positive square root, because }\theta \textsf{ is an}\\\textsf{acute angle, so its sine is positive)}\\\\ \mathsf{sin\,\theta=\dfrac{2}{\sqrt{13}}} \end{array}

________


\large\begin{array}{l} \textsf{From (i), we find the value of }\mathsf{cos\,\theta:}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{2}\,sin\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\diagup\!\!\!\! 2}\cdot \dfrac{\diagup\!\!\!\! 2}{\sqrt{13}}}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\sqrt{13}}}\\\\ \end{array}

________


\large\begin{array}{l} \textsf{Since sine and cosecant functions are reciprocal, we have}\\\\ \mathsf{sin\,2\theta\cdot csc\,2\theta=1}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{sin\,2\theta}\qquad\quad\textsf{(but }}\mathsf{sin\,2\theta=2\,sin\,\theta\,cos\,\theta}\textsf{)}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\,sin\,\theta\,cos\,\theta}}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\cdot \frac{2}{\sqrt{13}}\cdot \frac{3}{\sqrt{13}}}} \end{array}

\large\begin{array}{l} \mathsf{csc\,2\theta=\dfrac{~~~~1~~~~}{\frac{2\cdot 2\cdot 3}{(\sqrt{13})^2}}}\\\\ \mathsf{csc\,2\theta=\dfrac{~~1~~}{\frac{12}{13}}}\\\\ \boxed{\begin{array}{c}\mathsf{csc\,2\theta=\dfrac{13}{12}} \end{array}}\qquad\checkmark \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2150237


\large\textsf{I hope it helps.}


Tags: <em>trigonometry trig function cosecant csc double angle identity geometry</em>

</span>
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1) What is 20% of 20?<br> 2) what is 15 is what percent of 30?<br> 3) 50 is 50% of what?
N76 [4]

Hi there!

The word "of" is the same thing as a multiplication sign.

1)

20% = 0.2

0.2 × 20 = 4


2)

? × 30 = 15

divide each side of the equation by 30

? = 0.5

0.5 = 50%


3)

50% = 0.5

0.5 × ? = 50

divide each side of the equation by 0.5

? = 100


There you go! I really hope this helped, if there's anything just let me know! :)

7 0
2 years ago
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Describe a relationship in which it would be reasonable to have a negative number in the domain or
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Answer:

Relationship between temperature at different times of the day during the Winter period in places like Alaska and Minnesota in the USA.

Step-by-step explanation:

An example of a relationship that would have a negative number in the domain or range would be the relationship between the temperature at different times of the day during the snow period in the winter. It's well known that in places like Alaska and Minnesota in the USA, that during the winter when there's very heavy snow, the average temperature is usually below 0°C. The temperature is the dependent variable and is most likely negative in those 2 states and thus the range would have negative numbers.

7 0
3 years ago
A large bacterium measures 750 micrometers in diameter. One micrometer = 10 − 6 meters. How would you express the diameter of th
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Answer:

7.5 * 10^-4

Step-by-step explanation:

To express this, we will have to multiply 750 by the conversion unit

we have this as;

750 * 10^-6

750 = 7.5 * 10^2

so we have;

7.5 * 10^2 * 10^-6

= 7.5 * 10^(-6+2)

= 7.5 * 10^-4

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algol [13]

One-third of a number x is equal to 22 less than the number.

(1/3)x=x-22

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Vanderbilt Corporation, which utilizes a calendar year as its fiscal year, is the payee on a $12,000, 7%, 8-month note receivabl
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Given:
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Cash                                  12,560
          Notes Receivable                        12,000
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