QuestionComplete the trigonometric table for $30^{\circ}$ and verify if " $45^{\circ}$ " in $\sin(\theta)$ is an error.

Studdy Solution

STEP 1

Assumptions1. The angle $\theta$ is $30^{\circ}$ . The trigonometric functions we are considering are $\sin$ , $\cos$ , and $\tan$
3. The values in the table should correspond to the trigonometric values of the angle $30^{\circ}$

STEP 2

The value " $45^{\circ}$ " in the $\sin (\theta)$ row seems to be an error. The $\sin$ of an angle is a ratio, not another angle. Let's correct this by finding the correct value of $\sin (30^{\circ})$ .
The value of $\sin (30^{\circ})$ is well-known and is equal to $0.5$ .

STEP 3

Now, let's find the value of $\cos (30^{\circ})$ . The value of $\cos (30^{\circ})$ is also well-known and is equal to $\frac{\sqrt{3}}{2}$ .

STEP 4

Lastly, let's find the value of $\tan (30^{\circ})$ . The $\tan$ of an angle is the ratio of the $\sin$ of the angle to the $\cos$ of the angle.
$\tan (\theta) = \frac{\sin (\theta)}{\cos (\theta)}$

STEP 5

Plug in the values for $\sin (30^{\circ})$ and $\cos (30^{\circ})$ to calculate $\tan (30^{\circ})$ .
$\tan (30^{\circ}) = \frac{\sin (30^{\circ})}{\cos (30^{\circ})} = \frac{0.5}{\frac{\sqrt{3}}{2}}$

STEP 6

Calculate the value of $\tan (30^{\circ})$ .
$\tan (30^{\circ}) = \frac{0.5}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}$

STEP 7

Now, we can fill in the corrected and completed table\begin{tabular}{|c|c|c|} \hline $\theta$ & $30^{\circ}$ & \\ \hline $\sin (\theta)$ & $0.5$ \\ \hline $\cos (\theta)$ & $\frac{\sqrt{3}}{2}$ \\ \hline $\tan (\theta)$ & $\frac{1}{\sqrt{3}}$ \\ \hline\end{tabular}

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms