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Solve for $x$ if $\cos(x - 30^{\circ}) = 0.5$ where $x \in [-60^{\circ};120^{\circ}]$.
in Grade 12 Maths by Bronze Status (5.9k points) | 16 views

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x-30= arcos(0.5)= 60 degrees as reference angle

0.5 is positive and cos is positive in 1st and 4th quadrants

1st, x= 60 +30= 90 degrees

4th, x= 360-60 +30= 330 degrees

x= 90 degrees only [ -60;120]
by Diamond (85.5k points)
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cos (x - 30) = 0.5

x -30 = arccos 0.5

x = 60 +30

x = 90

-60 < x < 120; -60 < 90 < 120
by Wooden (1.5k points)

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