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
laila [671]
3 years ago
11

Cos^2x+cos^2(120°+x)+cos^2(120°-x)i need this asap. pls help me​

Mathematics
1 answer:
o-na [289]3 years ago
5 0

Answer:

\frac{3}{2}

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - \frac{1}{2} cosx - \frac{\sqrt{3} }{2} sinx

squaring to obtain cos² (120 + x)

= \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - \frac{1}{2}cosx + \frac{\sqrt{3} }{2}sinx

squaring to obtain cos²(120 - x)

= \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x + \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

= cos²x + \frac{1}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}(cos²x + sin²x) = \frac{3}{2}

                 

You might be interested in
PLS ANWSER ASAP IN TI<br> ED!!
NikAS [45]

Answer:

Option (2)

Step-by-step explanation:

x = 1 is represented by a solid point on a number line.

x > 1 is represented by an arrow starting from x = 1 towards infinity

If we mix both the properties, x ≥ will be represented by an arrow starting from a solid point at x = 1 and moving towards the values greater than one.

From the options given,

Arrow mentioned in Option (2) will be the correct representation of the inequality.

7 0
3 years ago
How many fluid ounces are in 3 pints?
Lunna [17]
There are 16 ounces in one pint. You multiply 16 by three, and you get 48 fluid ounces.
7 0
3 years ago
Read 2 more answers
Simplify the following expression 2[(7-3)^4 divided by 8] SHOW YOUR WORK! <br> someone pls help
kirill115 [55]

Answer:

64

Step-by-step explanation:

2(7-3)^4 divided by 8

2(4)^4 divided by 8

2(256) divided by 8

512 divided by 8

64

4 0
3 years ago
Read 2 more answers
Thomas bikes at a rate of 24 mi in 3 h. Thomas’s friend De’Monte bikes 9.5 mi each hour. De’Monte and Thomas are 105 mi apart an
Murrr4er [49]
6 hours
...............................
8 0
3 years ago
Scores on a test are normally distributed with a mean of 81.2 and a standard deviation of 3.6. What is the probability of a rand
Misha Larkins [42]

<u>Answer:</u>

The probability of a randomly selected student scoring in between 77.6 and 88.4 is 0.8185.

<u>Solution:</u>

Given, Scores on a test are normally distributed with a mean of 81.2  

And a standard deviation of 3.6.  

We have to find What is the probability of a randomly selected student scoring between 77.6 and 88.4?

For that we are going to subtract probability of getting more than 88.4 from probability of getting more than 77.6  

Now probability of getting more than 88.4 = 1 - area of z – score of 88.4

\mathrm{Now}, \mathrm{z}-\mathrm{score}=\frac{88.4-\mathrm{mean}}{\text {standard deviation}}=\frac{88.4-81.2}{3.6}=\frac{7.2}{3.6}=2

So, probability of getting more than 88.4 = 1 – area of z- score(2)

= 1 – 0.9772 [using z table values]

= 0.0228.

Now probability of getting more than 77.6 = 1 - area of z – score of 77.6

\mathrm{Now}, \mathrm{z}-\text { score }=\frac{77.6-\text { mean }}{\text { standard deviation }}=\frac{77.6-81.2}{3.6}=\frac{-3.6}{3.6}=-1

So, probability of getting more than 77.6 = 1 – area of z- score(-1)

= 1 – 0.1587 [Using z table values]

= 0.8413

Now, probability of getting in between 77.6 and 88.4 = 0.8413 – 0.0228 = 0.8185

Hence, the probability of a randomly selected student getting in between 77.6 and 88.4 is 0.8185.

4 0
3 years ago
Other questions:
  • Help please I'm not really understanding this
    15·1 answer
  • Factor<br> 6x2 – 17x – 14
    13·2 answers
  • 4k – 6 = -2k – 16 – 2
    12·1 answer
  • Find the length and width of a rectangle whose perimeter is
    11·1 answer
  • Jade has $451.89 in her checking account. After 3 checks, each for the same amount, are deducted from her account, she has $358.
    8·2 answers
  • Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=10
    11·1 answer
  • Jackson decides to distribute buttons to advertise the no-smoking campaign. He plans to make 700 buttons. Large buttons cost 75
    6·1 answer
  • Identify the conic section that the given equation represents<br> y+1=-1/20(x-2)^2
    10·1 answer
  • What is 2-2 equals to ?
    10·2 answers
  • A center pivot irrigation system provides water to a sector shaped field, find the area of the field if 0=140 degrees and r= 40
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!