Oliver

10-26-2013, 05:30 AM

Which of the following is the value of sin(x) given that sec(x)=\frac{5}{2}?

(A) \frac{\sqrt{21}}{5}

(B) \frac{\sqrt{21}}{2}

(C) \frac{\sqrt{5}}{2}

(D) \frac{\sqrt{5}}{21}

Thanks!

nicole

10-26-2013, 05:31 AM

We know that sec(x)=\frac{1}{cos(x)}.

So, sec(x)=\frac{1}{cos(x)}=\frac{5}{2} \Rightarrow cos(x)=\frac{2}{5}

From the following trigonometric identity

(sin(x))^2+(cos(x))^2=1

we can find the value of sin(x)

(sin(x))^2=1-(\frac{2}{5})^2 \Rightarrow sin(x)=\sqrt{1-\frac{4}{25}}=\sqrt{\frac{21}{25}}

sin(x)=\sqrt{\frac{21}{25}}= \frac{\sqrt{21}}{5}

Therefore the correct answer is (A).:)

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