1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
QveST [7]
3 years ago
5

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

Mathematics
1 answer:
AVprozaik [17]3 years ago
7 0

Answer:

D

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:

<h2>\displaystyle  \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}</h2>

Simplify:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}

Evaluate:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}

So, our answer is D.

You might be interested in
A coffee shop serves three times as many cups of regular coffee as decaffeinated coffee. If the shop serves d cups of decaffeina
galben [10]

Answer:

Number of cups of regular coffee the shop sells = 3d

Step-by-step explanation:

Let

d = cups of decaffeinated coffee

Three times as many cups of regular coffee as decaffeinated coffee.

Number of cups of regular coffee the shop sells = 3d

8 0
2 years ago
Use the slope to determine if lines AB and CD are parallel, perpendicular, or neither
ycow [4]
The slope of B is Q maybe
7 0
2 years ago
SOMEONE HELP ASAP PLEASEEEEE!!!!!
Murrr4er [49]

Answer:

the answer is 35% probability

your welcome

5 0
3 years ago
Dale has three dollars more than twice the amount of money that Leo has.
KATRIN_1 [288]
2+3+4+5+y+7+8+9+10c11+12+13+14+15
8 0
3 years ago
Read 2 more answers
I need help with this math
enot [183]

Answer:

question? haven't learn this yet but try asking desmos that app helps me a lot!

3 0
3 years ago
Other questions:
  • A locker requires a three-digit code to open the lock. The code must contain one letter and two numbers, and no letter or number
    15·2 answers
  • Use the following similar triangles (ABC ~ DEF). If AC= 18 when DF=19 and AB=15, what is DE? Solve mathematically. Round your an
    12·2 answers
  • On Tuesday Katy ran a mile in 8.34 minutes. She ran another mile in 7.89 minutes on Wednesday. What was the total time for both
    7·2 answers
  • What is the lcm of 9 and 12<br><br>*lmc* lowest common multiple​
    9·1 answer
  • A red token is worth twice as much as an orange token. An orange token is worth 5 less a yellow token. A yellow token is worth 1
    5·1 answer
  • | 2. On rectangle ABCD below, if A is located at
    7·1 answer
  • Find the surface area of the cylinder. Use 3.14 for P.
    11·1 answer
  • Your teacher gives you a graph of the parent function y = x^2 and the graph of another function. You notice that the new functio
    13·2 answers
  • Find the perimeter of the figure.<br><br> O 1610 cm<br> O162 cm<br> O116 cm<br> O 81 cm
    7·1 answer
  • Instructions: Interpret the function given in the context of the real-world situation described to answer the question.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!