I need help plz I don't get this problem

Mathematics

1 answer:

OlgaM077 [116]3 years ago

5 0

To find the answer you need to write equivalent fractions with larger denominators. If you multiply each fraction by 3/3 then your equivalent fractions would be

3/5 × 3/3 = 9/15
4/5 × 3/3 = 12/15

Now we have two fractions that are equivalent to the original fractions and we can easily see that 2 fractions between 9/15 and 12/15 would be...

10/15 and 11/15

(10/15 can reduce to 2/3 so your answers could also be 2/3 and 11/15)

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

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Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence: