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William
10-28-2013, 05:50 PM
Which of the following is the value of cos(x) given that cosec(x)=\frac{3}{2}?

(A) \frac{\sqrt{5}}{9}

(B) \frac{\sqrt{5}}{3}

(C) \frac{\sqrt{3}}{2}

(D) \frac{\sqrt{3}}{4}


Thanks!

Thomas
10-28-2013, 05:51 PM
We know that cosec(x)=\frac{1}{sin(x)}

So, cosec(x)=\frac{1}{sin(x)}=\frac{3}{2} \Rightarrow sin(x)=\frac{2}{3}

From the following trigonometric identity

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

we can find the value of cos(x)

(cos(x))^2=1-(\frac{2}{3})^2 \Rightarrow cos(x)=\sqrt{1-\frac{4}{9}}=\sqrt{\frac{5}{9}}

cos(x)=\sqrt{\frac{5}{9}}= \frac{\sqrt{5}}{3}

Therefore the correct answer is (B).:)

William
10-28-2013, 05:52 PM
We know that cosec(x)=\frac{1}{sin(x)}

So, cosec(x)=\frac{1}{sin(x)}=\frac{3}{2} \Rightarrow sin(x)=\frac{2}{3}

From the following trigonometric identity

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

we can find the value of cos(x)

(cos(x))^2=1-(\frac{2}{3})^2 \Rightarrow cos(x)=\sqrt{1-\frac{4}{9}}=\sqrt{\frac{5}{9}}

cos(x)=\sqrt{\frac{5}{9}}= \frac{\sqrt{5}}{3}

Therefore the correct answer is (B).:)

Thanks for your prompt response!!