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
VashaNatasha [74]
2 years ago
15

Solve the the equation tan(x+pi/3) = sqrt 3/3 over the interval [0, 2].

Mathematics
1 answer:
kupik [55]2 years ago
7 0

Rewrite the right side as √3/3 = 1/√3, and recall that tan(x) = 1/√3 when x = π/6. Then since tan is π-periodic, taking the inverse tan of both sides gives

\tan\left(x + \dfrac\pi3\right) = \dfrac1{\sqrt3} \implies \tan^{-1}\left(\tan\left(x + \dfrac\pi3\right)\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) + n\pi

\implies x + \dfrac\pi3 = \dfrac\pi6 + n\pi

where n is any integer. Solving for x, we get

x = -\dfrac\pi6 + n\pi

and the solutions in the interval [0, 2π] are x = 5π/6 and x = 11π/6 (for n = 1 and n = 2).

You might be interested in
There are 8 hamburger buns in a package. which number of hamburger buns would fill a whole number of packages: 18, 32, 44, 56?
olganol [36]

Answer:

32 and 56?

Step-by-step explanation:

32 and 56 are related to 8.

32=8x4

56=8x7

6 0
2 years ago
If f(x) = 2x6 + 3x5 – 1, then what is the remainder when f(x) is divided by<br> x + 1?
Alchen [17]
<h3>Answer:   -2</h3>

===============================================

Explanation:

We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).

Comparing x+1 to x-k shows that k = -1

It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.

Plug this k value into the function

f(x) = 2x^6 + 3x^5 - 1

f(-1) = 2(-1)^2 + 3(-1)^5 - 1

f(-1) = 2(1) + 3(-1) - 1

f(-1) = 2 - 3 - 1

f(-1) = -1 - 1

f(-1) =-2

The remainder is -2

We can confirm this through synthetic division or polynomial long division.

5 0
3 years ago
The graph of g(x) is the result of translating the graph of f(x) =  three units to the left. What is the equation of g(x)?
Marysya12 [62]
To translate it 3 to the left, g(x) = f(x+3)
7 0
3 years ago
Read 2 more answers
What is the sum of 3+(−4) = -1
Dmitry [639]
3+-4=-1
3-4=-1
-1=-1

so the answer is:
-1 = -1
8 0
2 years ago
Read 2 more answers
Please anybody can help me anyone i need your help to solve this question​
podryga [215]

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 21p^2 + 3qp

Explanation:

To find the area of the triangle you have to do LxHx1/2

Length = 7p+q

Height = 6p

(7p+q)*6p*1/2 = 21p^2+3qp

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

8 0
3 years ago
Read 2 more answers
Other questions:
  • (5.42x10^2)—(2.1x10^-1) simplify and solve in scientific notation and please show work
    13·1 answer
  • The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A de
    10·1 answer
  • A car breaks from a speed of 108km/h to 72km/h during a displacement of 100m, what is its aceleration ?​
    5·1 answer
  • Klein stated before 7:10 meg inlinewhich shows this distance written as a decimal
    6·1 answer
  • The cost of a pack of pencils is $3 while the cost of a pack of pens is $5.
    6·2 answers
  • 1. Use the distributive property to write 13y-(5x-3y)+x (can u also answer) 2. The state sales tax rate is 4.75% harold would li
    15·1 answer
  • mitt ate 24 peanuts this represents 75% of the bag of peanuts how many peanuts were originally in the bag
    7·2 answers
  • What is the slope of the line on the graph?
    10·2 answers
  • Plzzzzz helppppp this is due tonight
    6·1 answer
  • 2. Write an equation of the line in point-slope<br> form passing through (0,5) and (4,3).
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!