Question

Create trig ratios for sin, cos, and tan:

Answer 1

You can look the image.

It is very clear.

Answer 2

`\sin (Z)=\sf(9)/(15)`
`\cos (Z)=\sf(12)/(15)`
`\tan(Z)=\sf (9)/(12)`

Explanation:

To create trigonometric ratios for angle Z in the given right triangle XYZ, we can use the trigonometric ratios.

`\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

From inspection of the right triangle XYZ:

• θ = Z
• O = XY = 9
• A = YZ = 12
• H = XZ = 15

Substitute these values into the three ratios to create the trigonometric ratios for angle Z:

`\sin (Z)=\sf (O)/(H)=(9)/(15)`

`\cos (Z)=\sf (A)/(H)=(12)/(15)`

`\tan(Z)=\sf (O)/(A)=(9)/(12)`