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2 years ago

Please helpp meeee!!!!

Mathematics

1 answer:

nata0808 [166]2 years ago

6 0

Answer: The answer is because , hope this helps :)

Step-by-step explanation:

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

eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

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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: trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus

7 0

2 years ago

Need answers please ASAP detention

Airida [17]

PLAN
(2,4) and (2,-3)

SOLVE
. 2
. |4|= 4 |-3|= 3
. Distance from (2,4) to the x-axis= 6
. Distance from (2,-3) to the x-axis= -1
. 6 + (-1) = 5 blocks

8 0

3 years ago

Find the dimensions of a rectangle

gayaneshka [121]

The length of the shorter side is 7 longer side is 12 7+7+12+12 is 38 and 7x12 is 84

4 0

1 year ago

Find the domain of the following piece wise function

anastassius [24]

Answer:

Step-by-step explanation:

$f(x)=\left\{\begin{array}{ccc}x+4&if&-4\leq x$

8 0

2 years ago

Y=-x+1 y=2/3x-4 please answer this!!!!

yawa3891 [41]

Answer:

(x, y) = (-15, -14)

Step-by-step explanation:

y = x+1

y = 2/3x - 4

Next, we will substitute the value of y (first equation) into the second equation.

x+1 = 2/3x - 4

1/3x + 1 = -4

1/3x = -5

x = -15

So, y = -14

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2 years ago