Question

What is the value of sin 0 given that (-3,7) is a point on the terminal side 0

Answer 1

`(7√(58))/(58)`

Explanation:

`\\\text{Given that a point on the terminal side of }\theta \text{ is }(-3,7)\\\\\text{so the terminal side is in Quadrant II}\\\\\text{In the right triangle OMN, using Pythagorean theorem, we get}\\\\\text{ON}=√((MN)^2+(OM)^2)\\\\\Rightarrow ON=√((7)^2+(-3)^2)\\\\\Rightarrow ON=√(49+9)\\\\\Rightarrow ON=√(58)\\`

`\\\text{we know that in Quadrant II, sine and cosecant are positive.}\\\text{so using the trigonometric ratios, we get}\\\\\sin \theta=\frac{\text{Opposite }}{\text{Hypotenus}}\\\\\Rightarrow \sin \theta=(7)/(√(58))\\\\\Rightarrow \sin \theta=(7√(58))/(58)\\`