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3 years ago

Please help me get this question correct

Mathematics

1 answer:

TiliK225 [7]3 years ago

8 0

The answer is going to be C I think

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Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ>0

eduard

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$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: <em>trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus</em>

7 0

2 years ago

Natalie picked 135 berries in 15 minutes. If she continues picking at that rate, how many total minutes will it take her to pick

Alex777 [14]

Lets focus on what we know first. Natalie can pick 135 Berries in 15 minutes. Lets find out how many berries she can pick per minute.
In order to do so, We have to divide 135 by 15.

135/15=9
This means that Natalie can pick 9 berries per minute. Given that we want her to pick 486, we will need to divide that number by 9 berries to find out how many minutes it will take to get her to that number of berries.

486/9=54

This means that it will take Natalie 54 minutes in order to pick 486 berries.

5 0

3 years ago

Which angles are supplementary to each other?

user100 [1]

Answer:

Angles 2 and 3 are supplementary to each other

Step-by-step explanation:

A supplementary angle is 2 angles that when you add the sum is 180.

4 0

3 years ago

Marek thinks of 2 prime numbers that are larger than 3. He multiplies the 2 numbers together.is his answer odd or even.

Stolb23 [73]

Im thinking it would be odd because when you multiply 2 odd numbers youre result is usually odd

5 0

3 years ago

Read 2 more answers

Help out before 8pm <br><br> -geometry

Ira Lisetskai [31]

Answer:

(0, -1)

Step-by-step explanation:

((4 + (-4))/2, (2 + (-4))/2) =

(0/2, -2/2) =

(0, -1)

6 0

3 years ago