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Cerrena [4.2K]
3 years ago
6

Find the values of cosΘ and tanΘ, given that sinΘ = 8/9 and Θ is in quadrant I

Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0
sin^2 \alpha +cos^2 \alpha =1\ \ \ and\ \ \ tan \alpha = \frac{\big{sin \alpha }}{\big{cos \alpha }} \\\\sin \alpha  =  \frac{8}{9}\\\\ \Rightarrow\ \ \ (\frac{8}{9})^2+cos^2 \alpha =1\ \ \ \Rightarrow\ \ \ cos^2 \alpha =1- \frac{64}{81} \ \ \ \Rightarrow\ \ \ cos^2 \alpha = \frac{17}{81} \\\\ \alpha \ \in\ (0^0;90^0)\ \ \ \Rightarrow\ \ \ cos \alpha >0\ \ \ \Rightarrow\ \ \ cos \alpha = \frac{ \sqrt{17} }{9} \\\\

tan \alpha = \frac{8}{9}: \frac{ \sqrt{17} }{9} =\frac{8}{9}\cdot  \frac{9}{\sqrt{17}}= \frac{8}{\sqrt{17}}= \frac{8\cdot \sqrt{17}}{\sqrt{17}\cdot \sqrt{17}}=\frac{8\cdot \sqrt{17}}{17}
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Please help I need help with my hw
olga2289 [7]

Answer:

a) 2.5 pounds of candy

b) 2.5 pounds of candy

    \frac{0.5}{1} :\frac{y}{5}

    y × 1 = 0.5 × 5

    y = 2.5

Step-by-step explanation:

1 = 5

1/2 = y or 0.5 = y

\frac{0.5}{1} :\frac{y}{5}

y × 1 = 0.5 × 5

y = 2.5

7 0
3 years ago
Jamie put 8 squares together to make rectangle. There are 2 rows of squares. Each row had 4 squares. How many pairs of sides tou
777dan777 [17]
I believe the answer is ten pairs...
The two rows each have 3 pairs touching, and the four columns each have 1, which makes 2*3 + 4*1 = 10
4 0
3 years ago
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Will give brainlist whoever asks correctly
Semenov [28]

Answer:

The answer is B.-3/2

Please correct me If I am wrong

Step-by-step explanation:

I use \frac{rise}{run}

Also, you automatically know that the line is decreasing

4 0
2 years ago
What is the length of the segment connecting the points A(1,3) and B(6,5)?
Natalija [7]

Answer:

The answer is

<h2>\sqrt{29}  \:  \:  \: or \:  \:  \:5.38 \:  \:  \: units</h2>

Step-by-step explanation:

The length of the segment connecting two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(1,3) and B(6,5)

The length is

|AB|  =  \sqrt{ ({1 - 6})^{2} +  ({3 - 5})^{2}  }  \\  =  \sqrt{ ({ - 5})^{2}  + ( { - 2})^{2} }  \\  =  \sqrt{25 + 4}  \\  =  \sqrt{29}

We have the final answer as

\sqrt{29}  \:  \:  \: or \:  \:  \:5.38 \:  \:  \: units

Hope this helps you

3 0
2 years ago
Explain the steps necessary for solving the following equation. x^2-8x-20=0
kirza4 [7]
First factor the equation
(x-10)(x+2) = 0
Then solve for (x-10) and (x+2)
x=10
x=-2
8 0
3 years ago
Read 2 more answers
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