Question

Please help me with my test?

solve
`4 cos x = 0.8, -180 ≤ x ≤ 180`

Answer 1

`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`