Question

A straight line inserted at the origin terminates at the point (6, 7) as it sweeps out an angle θ in standard position. Which of the following corresponds to the evaluation of sinθ?

Answer 1

Applying the Pythagorean theorem, with a = 6 and b = 7 (the legs of the right triangle formed), the length of the hypotenuse c is:

`\begin{gathered} c^2=a^2+b^2 \\ c^2=6^2+7^2 \\ c^2=36+49 \\ c^2=85 \\ c=\sqrt[]{85} \end{gathered}`

By definition:

`\sin (angle)=\frac{\text{opposite}}{\text{hypotenuse}}`

In this case, the angle is θ, the hypotenuse is c and the opposite side is 7 units long. Substituting this information into the equation, we get:

`\sin \theta=\frac{7}{\sqrt[]{85}}`