Suppose A is the arc on the unit circle that connects $(1, 0)$ $(1,0)$ to $(- \frac{12}{13}, \frac{5}{13})$ $(-12/13, 5/13)$ and passes through $(0, - 1)$ $(0,-1)$ . Let $u$ $u$ be the measure of the angle that subtends this arc. Find the value of $sin (u)$ $sin(u)$ ?

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Suppose A is the arc on the unit circle that connects $(1, 0)$ $(1,0)$ to $(- \frac{12}{13}, \frac{5}{13})$ $(-12/13, 5/13)$ and passes through $(0, - 1)$ $(0,-1)$ . Let $u$ $u$ be the measure of the angle that subtends this arc. Find the value of $sin (u)$ $sin(u)$ ?

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Answer 1 · 2018-02-26T14:30:09

See below.

Explanation:

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If we pass through point $(0, - 1)$ $(0,-1)$ then we are rotating in a anti clockwise direction.

We can see by the coordinates $(- \frac{12}{13}, \frac{5}{13})$ $(-12/13,5/13)$ that the terminal side is in the II quadrant. The $y$ $y$ coordinate $\frac{5}{13}$ $5/13$ is the sine ratio for the angle that is formed with the negative $x$ $x$ axis, which will be $arcsin (\frac{5}{13})$ $arcsin(5/13)$ , but we have rotated through the IV and III quadrants, so our angle $u$ $bbu$ will be $- arcsin (\frac{5}{13}) - π \approx - 3.536383774 8888$ $-arcsin(5/13)-pi~~-3.536383774color(white)(8888)$ radians or $- {202.62}^{\circ}$ $-202.62^@$ .

I have given the angle as a negative rotation, but in angles subtended by arcs this is usually given as a positive angle .i.e. $3.53638377$ $3.53638377$ radians.

$sin (u) = sin (- arcsin (\frac{5}{13}) - π) \approx 0.3846153846$ $sin(u)=sin(-arcsin(5/13)-pi)~~0.3846153846$

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Suppose A is the arc on the unit circle that connects $(1, 0)$ $(1,0)$ to $(- \frac{12}{13}, \frac{5}{13})$ $(-12/13, 5/13)$ and passes through $(0, - 1)$ $(0,-1)$ . Let $u$ $u$ be the measure of the angle that subtends this arc. Find the value of $sin (u)$ $sin(u)$ ?

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Explanation:

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Explanation:

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Suppose A is the arc on the unit circle that connects $(1, 0)$ $(1,0)$ to $(- \frac{12}{13}, \frac{5}{13})$ $(-12/13, 5/13)$ and passes through $(0, - 1)$ $(0,-1)$ . Let $u$ $u$ be the measure of the angle that subtends this arc. Find the value of $sin (u)$ $sin(u)$ ?