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
Orlov [11]
3 years ago
15

If cos(x)cos(π/7)+sin(x)sin(π/7)= - (√2)/2, then x can equal:

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
8 0

\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\

\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}

You might be interested in
Minh wants to buy a car costing $9,950. She can put $1,000 down and finance the rest at 10.9% APR, making the monthly payments f
son4ous [18]

Answer:

piip;[-p-o-ul0i

Step-by-step explanation:

6 0
2 years ago
Trains Two trains, Train A and Train B, weigh a total of 360 tons. Train A is heavier than Train B. The difference of their weig
Sergio [31]
Since both trains in total weigh 360 tons and train A weighs more than train be, it means that train B is the rest of the weight when you subtract train A from the total amount. Difference means subtraction so just solve this: 360-272 to get train B and you already know that train A is 272 tons. Please mark branliest!


8 0
3 years ago
Carlos is tiling a kitchen counter that is 12 feet by 3 feet.The counter has a rectangular hole 3 feet by 2 feet cut in it for a
alina1380 [7]

Answer:

Carlos has to tile 30 sq ft


3 0
3 years ago
Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?
vovangra [49]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

2 \times  \frac{1}{2} hour = 1hour \\

Thus ;

2 \times  \frac{5}{12}  \:  \: miles =  \frac{10}{12}  \:  \: miles = \frac{5}{6}  \:  \: miles  \\

,♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

6 0
2 years ago
Read 2 more answers
What is the median value of the data set shown on the line plot? Enter your answer in the box. A line plot with twenty-two data
Bogdan [553]
Answer: the median is 6.

Please see the picture attached.

A line plot shows the number of occurrences (crosses) of each number of a data set.

The median is the central value, the middle number, of a data set ordered from least to greatest. When there are two middle numbers, the median will be the mean between the two.

In order to find the median, look at the line plot: count how many values you have (22), then add 1 (23) and divide by two (11.5). Since we have an even number of values, we will have two middle numbers, which will be in the eleventh and twelfth position.

Count the crosses from the left, the eleventh and twelfth crosses both correspond to the number 6, therefore the median is 6.

You can also write all the numbers in increasing order and divide them into two equal groups:
1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6 | 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 11

The median will be the average between the two central numbers, therefore 6 (again).


8 0
3 years ago
Read 2 more answers
Other questions:
  • Jennys lawn is 1/3 of an acre. after mowing 1/2 of the lawn, how much of an acre has she mowed
    14·1 answer
  • Divide and simplify 3/4÷2/3
    10·1 answer
  • What 2 numbers add up to 37 and multiply to -210?
    11·1 answer
  • In how many ways is it possible to sit 8 people at a round table if Alex and Bob
    14·1 answer
  • What was the first year that the amusement park had more than 12 million visitors?
    12·1 answer
  • Help me somebody plssss
    14·1 answer
  • If a light ray is relflected off the shiny surface at 170 degrees, at what angle did the light ray first strike the surface?
    13·1 answer
  • Can someone help me with this two because I am very confused
    9·2 answers
  • Which of the following relations is not a function ?
    8·1 answer
  • Has a slope of 4 and passes through (-2, 4)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!