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If sin(theta)=3/5 and tan is less than theta, what is the value of sec(2theta)

 Jun 1, 2015

Best Answer 

 #1
avatar+118723 
+5

If sin(theta)=3/5 and tan is less than theta, what is the value of sec(2theta)

I have no idea what "tan is less than theta" even  means 

BUT

  $$\\If\qquad sin\theta=\frac{3}{5}=0.6 \qquad then \qquad cos\theta=\pm \frac{4}{5}=0.8\\\\
sec2\theta \\\\
= \frac{1}{cos2\theta}\\\\
= \frac{1}{cos^2\theta - sin^2 \theta}\\\\
= \frac{1}{0.64 - 0.36}\\\\
= \frac{1}{0.28}\\\\
= \frac{100}{28}\\\\$$

 

$${\frac{{\mathtt{100}}}{{\mathtt{28}}}} = {\frac{{\mathtt{25}}}{{\mathtt{7}}}} = {\mathtt{3.571\: \!428\: \!571\: \!428\: \!571\: \!4}}$$

 Jun 2, 2015
 #1
avatar+118723 
+5
Best Answer

If sin(theta)=3/5 and tan is less than theta, what is the value of sec(2theta)

I have no idea what "tan is less than theta" even  means 

BUT

  $$\\If\qquad sin\theta=\frac{3}{5}=0.6 \qquad then \qquad cos\theta=\pm \frac{4}{5}=0.8\\\\
sec2\theta \\\\
= \frac{1}{cos2\theta}\\\\
= \frac{1}{cos^2\theta - sin^2 \theta}\\\\
= \frac{1}{0.64 - 0.36}\\\\
= \frac{1}{0.28}\\\\
= \frac{100}{28}\\\\$$

 

$${\frac{{\mathtt{100}}}{{\mathtt{28}}}} = {\frac{{\mathtt{25}}}{{\mathtt{7}}}} = {\mathtt{3.571\: \!428\: \!571\: \!428\: \!571\: \!4}}$$

Melody Jun 2, 2015

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