Solving trigonometric equations graphically CKI

Given the diagram shown, choose the equation below which has solutions x₁ and x₂

• 2cosx – 3sinx = 0

• 2cosx + 3sinx = 0

• 2cosx = 3sinx

• 3cosx = 2sinx

Given the diagram, the points A and B shown in red are the solutions to:

•  $y=\cosθ\ and\ y=-\sqrt{\frac{3}{2}}$  

•  $\cosθ=\sqrt{\frac{3}{2}}$  

•  $\cosθ-\sqrt{\frac{3}{2}}=0$  

•  $y=\cosθ\ and\ y=\sqrt{\frac{3}{2}}$  

The diagram shows the solutions to

• $\sin x=\cos3x$

• $\sin x=\cos x$

• $\sin⁡x+\cos⁡3x=0$

• $\sin x=3\cos x$

State the number of solutions to  

 $\sin x=\cos3x,\ \ \ [0,π]$  

• 6

• 5

• 4

• 3

The diagram show the solutions to

•  $\cos⁡x=\frac{3}{4}\ for\ \ [0°,360°]$  

•  $\cos2⁡x=\frac{3}{4}\ for\ \ [0°,360°]$  

•  $2\cos⁡x=\frac{3}{4}\ for\ \ [0°,360°]$  

•  $\cos⁡x=\frac{3}{4}\ for\ \ [-360°,\ 360°]$  

The diagram shown could be used to indicate the solutions to:

•  $3\cos x=4$ 

•  $3\cos x+4=4$ 

•  $-3\cos2x+4=4$ 

•  $-3\cos x+4=4$ 

The diagram shows the solutions to  $y=\sin\theta,\ \ y=\sin2\theta,\ \ y=\sin\frac{\theta}{2}$  
The number of solutions to
 $\sin2\theta=\sin\frac{\theta}{2},\ \left[0,\ 2\pi\right]$  is

• 3

• 4

• 5

• 6

Given the diagram shown of  y=5sin 2x+4, the number of solutions to   5sin2x - 5= 0,   [0,360] is:

• 2

• 3

• 4

• 5

 $The\ diagram\ shows\ the\ graph\ of\ f(x)=\sin x-\frac{1}{2}$  The two red dots indicate the solutions to:

•  $\sin x-\frac{1}{2}=0$  

•  $\sin x=-\frac{1}{2}$  

•  $\sin x=0$  

•  $y=\sin x-\frac{1}{2}$  

The diagram shows the solutions to:

• $\sin x=-\frac{1}{2}$

• $\sin x=-1$

• $\cos x=-1$

• $\cos x=-1/2$