Advanced Trigonometry, 2ADV T2 2023 HSC 20 Find all the values of `theta`, where `0^@ <=theta <= 360^@`, such that `sin(theta-60^@)=-sqrt3/2` (3 marks) --- 6 WORK AREA LINES (style=lined) --- Show Answers Only `theta=0^@, 300^@ and 360^@` Show Worked Solution `sin60^@=sqrt3/2\ \ =>\ \ text{Reference angle}\ =60^@` `=>\ text{sin is negative in 3rd and 4th quadrants}` `sin(theta-60^@)` `=180+60, 360-60` `=240^@, 300^@` `theta-60^@=240^@\ \ =>\ \ theta=300^@` `theta-60^@=300^@\ \ =>\ \ theta=360^@` `text{Consider}\ theta = 0^@` `sin(0-60^@)=sin(-60^@)=-sqrt3/2` `:.theta=0^@, 300^@ and 360^@`