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
Lorico [155]
2 years ago
12

Can anyone explain those marked steps in case (iii)

Mathematics
1 answer:
Tema [17]2 years ago
5 0
\cos\dfrac{3x}2=\cos\left(\dfrac\pi2+\dfrac x2\right)
\implies \dfrac{3x}2=2n\pi+\dfrac\pi2+\dfrac x2

follows from the fact that the cosine function is 2\pi-periodic, which means \cos x=\cos(2\pi+x). Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add 2\pi to the original point's angle with respect to the horizontal axis).

If you make another complete revolution (so we're effectively adding 4\pi) we get the same result: \cos x=\cos(4\pi+x). This is true for any number of complete revolutions, so that this pattern holds for any even multiple of \pi added to the argument. Therefore \cos x=\cos(2n\pi+x) for any integer n.

Next, because \cos(-x)=\cos x, it follows that \cos x=\cos(2n\pi-x) is also true for any integer n. So we have

\implies \dfrac{3x}2=2n\pi\pm\left(\dfrac\pi2+\dfrac x2\right)

The rest follows from considering either case and solving for x.
You might be interested in
State the transformations on the graph of f(x) = ^ x that result in the graph of the given functions.
Alex_Xolod [135]
The answer is 9/10 because I did the test and that was the answer
4 0
2 years ago
Answer with a complete sentence. Eric and Jan leave their house at one o-clock, following the same route. Jan walks at a steady
xenn [34]

Answer:

Eric will catch up with Jan at 3 o-clock.

Idk I really tried sorry if its wrong lol

7 0
2 years ago
A political gathering in South America was attended by 7,910 people. Each of South America’s 14 countries was equally represente
zheka24 [161]

Answer:

565

Step-by-step explanation:

You would divide the number of people (7910) by the number of countries attending (14).

7910÷14=565

3 0
3 years ago
What is 3pairs of numbers that have 5 as their greatest common factor
cupoosta [38]
10, 20 , 30, 45 has 5 as their greatest common factor

6 0
2 years ago
Ugh ,, im stuck again :( someone please explain this !!!
EastWind [94]

Answer:

63cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the two triangles

Area of the rectangle = 6(3+14)

Area of the rectangle = 6 * 17

Area of the rectangle = 102cm²

Area of the smaller triangle = 1/2 * 3 * 6

Area of the smaller triangle = 18/2 = 9cm²

Area of the larger triangle = 1/2 * 6 * (17-7)

Area of the larger triangle = 1/2 * 6 * 10

Area of the larger triangle = 60/2 = 30cm²

Area of the shaded part = 102 - (9+30)

Area of the shaded part = 102 - 39

Area of the shaded part = 63cm²

3 0
2 years ago
Other questions:
  • Help me please!!!
    15·2 answers
  • Help meeeee please <br> Geometry
    8·1 answer
  • What kind of number is the square root of 48​
    6·2 answers
  • I need help with the grape.
    6·1 answer
  • If you toss four fair coins, in how many ways can you obtain at least one head? Group of answer choicesA. 1/16B. 1/2C. 3/16D. 11
    14·1 answer
  • If f(x)= x+4/x, g(x) = x-2, and h(x)= 4x-1, what is (fohog)
    13·1 answer
  • bill took a nap for 1 1/4 hour on friday and then took a nap for 3/4 hour on tuesday. how much longer was Bill's nap on friday?
    8·2 answers
  • John's phone bills for the last five months are $24.71, $22.13, $19.87, $27.33, and $26.76.
    6·1 answer
  • Find the volume of the prism
    10·2 answers
  • (x-1)^3-x^2(x+3)=2<br><br> Find x<br> send help
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!