smc-6411-30-tan

Trigonometry, 2ADV EQ-Bank 5

Find the exact value of

\(\sin 240^{\circ}\) (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
\(\tan \left(-120^{\circ}\right)\) (1 mark)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

a. \(-\dfrac{\sqrt{3}}{2}\)

b. \(\sqrt{3}\)

Show Worked Solution

a. \(\sin 240^{\circ}=\sin (180+60)=-\sin 60^{\circ}=-\dfrac{\sqrt{3}}{2}\)

b. \(\tan \left(-120^{\circ}\right)=\tan 240^{\circ}\)

\(\tan 240^{\circ}=\tan (180 + 60)=\tan 60^{\circ}=\sqrt{3}\)

Find the exact value of

Show Answers Only

a. \(-\dfrac{1}{\sqrt{3}}\)

b. \(-\dfrac{\sqrt{3}}{2}\)

Show Worked Solution

a. \(\tan 330^{\circ}=\tan (360-30)=-\tan 30^{\circ}=-\dfrac{1}{\sqrt{3}}\)

b. \(\cos 510^{\circ}=\cos 150^{\circ}\)

\(\cos 150^{\circ}=\cos (180-30)=-\cos 30^{\circ}=-\dfrac{\sqrt{3}}{2}\)

What are the solutions of `sqrt3 tanx = -1` for `0<=x<=2 pi`?

Show Answers Only

`D`

Show Worked Solution

`sqrt3 tanx`	`= -1`
`tanx`	`= -1/sqrt3`

`text(When)\ tanx = 1/sqrt3,\ \ x=pi/6`

`text(S)text(ince)\ tanx\ text(is negative in)\ 2^text(nd) // 4^text(th)\ text(quadrant)`

`:. x`	` = pi\-pi/6,\ 2 pi\-pi/6,\ …`
	`= (5 pi)/6,\ (11 pi)/6`

`=> D`