Maths A level, trigonometric functions

Solve (i) cos(theta + 70) = 0.5 for 0 _< X _< 360
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So I understand the method however I don't know why they only used subtracted or divided from 360 rather than 180 as well as both values from 180 (180+60 and 180-60) would still fit in the bracket of 70 _< x _< 430. There are some other questions where you figure out the solution to the equation and you use 180 instead of 360 so I am confused as to the difference.

(edited 6 months ago)

Reply 1

davros

Original post by Boggatus

Solve (i) cos(theta + 70) = 0.5 for 0 _< X _< 360
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I can't open your attachment - it wants a gmail login - but are you getting confused between sin and cos? Note that sin and cos both have period 360 degrees i.e. sin(360 + x) = sin x and cos(360 + x) = cos x, but sin has an additional symmetry sin(180 -x ) = sin x (look at the shape of the grah for 0 <= x <= 180).

For cos, note that because it is an even function, cos(360 - x) = cos(360 + (-x)) = cos(-x) = cos x.