Question

11. If a point on a circle has a cos of theta equals 12/13 AND tan of theta is less than zero, then sin of theta equals 5/13 true or false?

Answer 1

True

Explanation

Step 1

$\cos \theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}$

then

$\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}=\frac{12}{13} \\ \\ \frac{adjacent\text{ side}}{\text{hypotenuse}}=\frac{12}{13} \\ \text{adjacent side=12} \\ \text{hypotenuse}=13 \end{gathered}$

Step 2

find y,use Pythagoras theorem

$\begin{gathered} a^2+b^2=c^2 \\ 12^2+y^2=13^2 \\ y^2=13^2-12^2 \\ y^2=25 \\ \sqrt[]{y^2}=\sqrt[]{25} \\ y=5 \end{gathered}$

Step 3

find sine of theta

$\begin{gathered} \sin \text{ }\theta=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \text{replace} \\ \sin \text{ }\theta=\frac{y}{13} \\ \sin \text{ }\theta=\frac{5}{13} \end{gathered}$

so, the answer is

TRUE

I hope this helps you