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

Step-by-step explanation

Step 1

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

then

`\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{\text{hypotenuse}}=(12)/(13) \\ \\ \frac{adjacent\text{ side}}{\text{hypotenuse}}=(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=(y)/(13) \\ \sin \text{ }\theta=(5)/(13) \end{gathered}`

so, the answer is

TRUE

I hope this helps you