How do you find $sin θ$ $sintheta$ and $cos θ$ $costheta$ if the terminal side of $θ$ $theta$ lies along the line $y = 2 x$ $y=2x$ in QI?

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How do you find $sin θ$ $sintheta$ and $cos θ$ $costheta$ if the terminal side of $θ$ $theta$ lies along the line $y = 2 x$ $y=2x$ in QI?

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Answer 1 · 2018-04-29T16:56:08

The slope, m, of the line $y = 2 x$ $y = 2x$ is, $m = 2$ $m =2$ .

For this line, we know that any ordered pair of coordinates will form a right triangle, therefore, we can choose any point and use the Pythagorean Theorem to compute the hypotenuse:

$h^{2} = x^{2} + y^{2}$ $h^2 = x^2+y^2$

Let's choose the point $(1, 2)$ $(1,2)$ :

$h^{2} = 1^{2} + 2^{2}$ $h^2 = 1^2+2^2$

$h^{2} = 1 + 4$ $h^2 = 1+4$

$h^{2} = 5$ $h^2 = 5$

$h = \sqrt{5}$ $h = sqrt5$

We know that:

$sin (θ) = \frac{y}{h}$ $sin(theta) = y/h$

$sin (θ) = \frac{2}{\sqrt{5}}$ $sin(theta) = 2/sqrt5$

Rationalize the denominator:

$sin (θ) = 2 \frac{\sqrt{5}}{5}$ $sin(theta) = 2sqrt5/5$

We know that:

$cos (θ) = \frac{x}{h}$ $cos(theta) = x/h$

$cos (θ) = \frac{1}{\sqrt{5}}$ $cos(theta) = 1/sqrt5$

Rationalize the denominator:

$cos (θ) = \frac{\sqrt{5}}{5}$ $cos(theta) = sqrt5/5$

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How do you find $sin θ$ $sintheta$ and $cos θ$ $costheta$ if the terminal side of $θ$ $theta$ lies along the line $y = 2 x$ $y=2x$ in QI?

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Humanities

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How do you find sinθsintheta and cosθcostheta if the terminal side of θtheta lies along the line y=2xy=2x in QI?

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How do you find $sin θ$ $sintheta$ and $cos θ$ $costheta$ if the terminal side of $θ$ $theta$ lies along the line $y = 2 x$ $y=2x$ in QI?