Friday, 9 October 2015

trigonometry - can't seem to understand $sin{theta} = y$ on a unit circle



So I've been working very hard on my trigonometry on khan academy. However I'm constantly getting stumped by one type of question in particular.




There is some fundamental flaw in my understanding.



I know what the unit circle is completely and why $\sin{\theta} = y$, however, in the following question I completely DO NOT understand why the answer wasn't B and G. The answer apparently was only G!



Why Isn't the y co-ordinate of $B = \sin{\theta}$ ?



enter image description here


Answer



The line segment $OG$ is at an angle of $\theta$ from the positive $x$-axis, whilst the line segment $OB$ is at an angle of $\theta$ from the negative $x$-axis and hence an angle of $\pi + \theta$ from the positive $x$-axis, so that the $y$-coordinate of $B$ is $\sin(\pi + \theta) = -\sin(\theta)$.


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