Question 1

Find all solutions  $cosx=\frac{\sqrt3}{2}$

Accepted Answer

$x=\frac{\pi}{6}  + 2n\pi$   or $x=\frac{11\pi}{6}  + 2n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$    or $x=\frac{5\pi}{3}  + 2n\pi$

Answer

$x=\frac{2\pi}{3}  + 2n\pi$   or $x=\frac{4\pi}{3}  + 2n\pi$

Answer

$x=\frac{5\pi}{6}  + 2n\pi$   or $x=\frac{7\pi}{6}  + 2n\pi$

Question 2

Find all solutions  $sinx=-\frac{\sqrt2}{2}$

Accepted Answer

$x=\frac{5\pi}{4}  + 2n\pi$  or $x=\frac{7\pi}{4}  + 2n\pi$

Answer

$x=\frac{3\pi}{4}  + 2n\pi$   or $x=\frac{5\pi}{4}  + 2n\pi$

Answer

$x=\frac{4\pi}{3}  + 2n\pi$    or $x=\frac{5\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$  or $x=\frac{5\pi}{3}  + 2n\pi$

Question 3

Find all solutions  $tanx=\sqrt3$

Accepted Answer

$x=\frac{\pi}{3}  + n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{4}  + n\pi$

Answer

$x=\frac{\pi}{4}  + 2n\pi$

Question 4

Find all solutions $tanx=0$

Accepted Answer

$x=0+ n\pi$

Answer

$x=\frac{\pi}{4}  + n\pi$

Answer

$x=\frac{3\pi}{2}  + n\pi$

Answer

$x=\frac{\pi}{2}  + n\pi$

Question 5

Find all solutions  $2sinx+\sqrt3=0$

Accepted Answer

$x=\frac{4\pi}{3}  + 2n\pi$  or $x=\frac{5\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$    or $x=\frac{2\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{4}  + 2n\pi$  or $x=\frac{3\pi}{4}  + 2n\pi$

Answer

$x=\frac{3\pi}{4}  + 2n\pi$   or $x=\frac{5\pi}{4}  + 2n\pi$

Question 6

Find all the solutions $2cosx+1=0$

Accepted Answer

$x=\frac{2\pi}{3}  + 2n\pi$  or $x=\frac{4\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{6}  + 2n\pi$    or $x=\frac{11\pi}{6}  + 2n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$   or $x=\frac{5\pi}{3}  + 2n\pi$

Answer

$x=\frac{5\pi}{6}  + 2n\pi$  or $x=\frac{7\pi}{6}  + 2n\pi$

Question 7

Find all solutions  $5sinx+1=3sinx$

Accepted Answer

$x=\frac{7\pi}{6}  + 2n\pi$  or $x=\frac{11\pi}{6}  + 2n\pi$

Answer

$x=\frac{\pi}{3}  + 2n\pi$  or $x=\frac{2\pi}{3}  + 2n\pi$

Answer

$x=\frac{4\pi}{3}  + 2n\pi$    or $x=\frac{5\pi}{3}  + 2n\pi$

Answer

$x=\frac{\pi}{6}  + 2n\pi$   or $x=\frac{5\pi}{6}  + 2n\pi$

Question 8

Find all solutions  $3sinx+5=-2sinx$

Accepted Answer

$x=\frac{3\pi}{2}  + 2n\pi$

Answer

$x=\pi+ 2n\pi$

Answer

$x=\frac{\pi}{2}  + 2n\pi$

Answer

$x=0+ 2n\pi$

Question 9

Solve:  $2sin^2x+sinx-1=0$

Accepted Answer

$x=\frac{\pi}{6}$, $x=\frac{5\pi}{6} $ , $x=\frac{3\pi}{2}$

Answer

$x=\frac{\pi}{3}$, $x=\frac{2\pi}{3} $ , $x=\frac{\pi}{2}$

Answer

$x=\frac{\pi}{3}$, $x=\frac{2\pi}{3} $ , $x=\frac{3\pi}{2}$

Answer

$x=\frac{\pi}{6}$, $x=\frac{5\pi}{6} $ , $x=\frac{\pi}{2}$

Question 10

Solve:  $cos^2x-1=0$

Accepted Answer

$x=0$, $x=\pi$

Answer

$x=\frac{\pi}{4}$, $x=\frac{3\pi}{4} $

Answer

$x=\frac{\pi}{2}$, $x=\frac{3\pi}{2} $

Answer

$x=\frac{\pi}{3}$, $x=\frac{2\pi}{3} $

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