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Svetllana [295]
3 years ago
15

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

Mathematics
1 answer:
aliina [53]3 years ago
8 0

Answer:

\frac{7\sqrt{58}}{58}

Step-by-step 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}=\sqrt{(MN)^2+(OM)^2}\\\\\Rightarrow ON=\sqrt{(7)^2+(-3)^2}\\\\\Rightarrow ON=\sqrt{49+9}\\\\\Rightarrow ON=\sqrt{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=\frac{7}{\sqrt{58}}\\\\\Rightarrow \sin \theta=\frac{7\sqrt{58}}{58}\\

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emmainna [20.7K]

Answer:

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Step-by-step explanation:

The given series is 26 + 24.5 + 23 + 21.5 + ... - 17.5

The first term of this series is a=26

The common difference is d=24.5-26=-1.5

The last term of the series is -17.5

The nth term is given by:

u_n=a+d(n-1)

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