Advanced Trigonometry, 2ADV T2 2023 HSC 20v2

Find all the values of `theta`, where `0^@ <=theta <= 360^@`, such that

`sin(theta-30^@)=-1/2` (3 marks)

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`theta=0^@, 240^@ and 360^@`

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`sin30^@=1/2\ \ =>\ \ text{Reference angle}\ =30^@`

`=>\ text{sin is negative in 3rd and 4th quadrants}`

`sin(theta-30^@)`	`=180+30, 360-30`
	`=210^@, 330^@`

`theta-30^@=210^@\ \ =>\ \ theta=240^@`

`theta-30^@=330^@\ \ =>\ \ theta=360^@`

`text{Consider}\ theta = 0^@`

`sin(0-30^@)=sin(-30^@)=-1/2`

`:.theta=0^@, 240^@ and 360^@`