Question

If sin x=−1/2, and 270°*
If 180°<θ<270°, and sinθ=−3/4, what is the value of sin(−θ)?

Answer 1

Note that the sin of an angle that will give a result of √2/2 are

`(1)/(4)\pi\quad and\quad (3)/(4)\pi`

So we need to equate the angle to those value above.

From the problem, we have :

`\sin (5x-\pi)=\frac{\sqrt[]{2}}{2}`

Equate the angle :

`\begin{gathered} 5x-\pi=(1)/(4)\pi \\ 5x=(1)/(4)\pi+\pi \\ 5x=(5)/(4)\pi \\ x=(5)/(20)\pi=(1)/(4)\pi \end{gathered}`
`\begin{gathered} 5x-\pi=(3)/(4)\pi \\ 5x=(3)/(4)\pi+\pi \\ 5x=(7)/(4)\pi \\ x=(7)/(20)\pi \end{gathered}`

The solutions are :

`\mleft\lbrace(\pi)/(4),(7\pi)/(20)\mright\rbrace`

The answer is B.