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Solution 4.2:4b

From Förberedande kurs i matematik 1

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We start by subtracting 2 from 113, so that we get an angle between 0 and 2. This doesn't change the cosine value

cos311=cos3112=cos35. 

Then, by rewriting 53 as a sum of - and 2-terms,

35=33+23+21=+2+6

we see that 53 is an angle in the fourth quadrant which makes an angle 6 with the negative y-axis.

With the help of an auxiliary triangle and a little trigonometry, we can determine the coordinates for the point on a unit circle which corresponds to the angle 53.

Image:4_2_4_b2.gif oppositeadjacent=1sin6=21=1cos6=23

The point has coordinates (1232)  and

cos311=cos35=21.