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4 cos x = 0.8, -180 ≤ x ≤ 180

1 Answer
Jan 27, 2018

x = -78.5^@, 78.5^@, -180<=x<=180

Explanation:

4 cos x = 0.8

cos x = 0.8/4

cos x = 0.2

cos^-1 (0.2) = 78.5^@ (3s.f.)

there are 2 values for x that can be found when x is in a range of 360^@.

when 0^@<=x<=360^@, x = 78.5^@ or 360^@ - 78.5^@

360 - 78.5 = 281.5

x = 78.5^@, 281.5^@ , 0<=x<=360

since the graph of y = cos x repeats itself every 360^@, the second value can be found by subtracting 360^@ from 281.5^@.

281.5-360 = -78.5

x = -78.5^@, 78.5^@, -180<=x<=180