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#4 cos x = 0.8, -180 ≤ x ≤ 180#

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Answer 1 · 2018-01-27T17:04:42

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

#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#