Geometry sem 1 7.1.2 Exam: Semester 1 Exam

Mathematics

1 answer:

Alex777 [14]3 years ago

6 0

Answer:

Step-by-step explanation:

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8/3

Step-by-step explanation:

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Solve the inequality 12(1/2×-1/3)>8-2x<br><br><br>

lianna [129]

Answer:

x > 3/2

Step-by-step explanation:

Simply the expression and get 6x - 4 > 8 - 2x

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Find sin(2x), cos(2x), and tan(2x) from the given information.

larisa86 [58]

Since $\cot(x)=\frac{2}{3}$ and $\cot^{2} x+1=\csc^{2} x$ , we know that:

$\left(\frac{2}{3} \right)^{2}+1=\csc^{2} x\\\\\frac{13}{9}=\csc^{2} x\\\\\csc x=\frac{\sqrt{13}}{3}$

If $\csc x=\frac{\sqrt{13}}{3}$ , this means that $\sin x=\frac{3}{\sqrt{13}}$ and by the Pythagorean identity,

$\sin^{2} x+\cos^{2} x=1\\\left(\frac{3}{\sqrt{13}} \right)^{2}+\cos^{2} x=1\\\frac{9}{13}+\cos^{2} x=1\\\cos^{2} x=\frac{4}13}\\\cos x=\frac{2}{\sqrt{13}}$

Using the double angle formula for sine, $\sin(2x)=2\left(\frac{3}{\sqrt{13}} \right)\left(\frac{2}{\sqrt{13}} \right)=\boxed{\frac{12}{13}}$
Using the double angle formula for cosine, $\cos(2x)=1-2\left(\frac{3}{\sqrt{13}} \right)^{2}=\boxed{-\frac{5}{13}}$
So, since tan=sin/cos, $\tan (2x)=\frac{\sin(2x)}{\cos(2x)}=\frac{\frac{12}{13}}{-\frac{5}{13}}=\boxed{-\frac{12}{5}}$