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
Rainbow [258]
3 years ago
6

Find all solutions of the equation in the interval (0,2π) cot theta +root 3 = 0

Mathematics
1 answer:
Alisiya [41]3 years ago
7 0

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.

You might be interested in
Need help! :(((((((((((((((((((((((((
Vlada [557]

Answer:

\frac{1}{8}

Step-by-step explanation:

it's so simple dude

4 0
2 years ago
Luiza is jumping on a trampoline.
lyudmila [28]

Answer:

The second time when Luiza reaches a height of 1.2 m = 2 08 s

Step-by-step explanation:

Complete Question

Luiza is jumping on a trampoline. Ht models her distance above the ground (in m) t seconds after she starts jumping. Here, the angle is entered in radians.

H(t) = -0.6 cos (2pi/2.5)t + 1.5.

What is the second time when Luiza reaches a height of 1.2 m? Round your final answer to the nearest hundredth of a second.

Solution

Luiza is jumping on trampolines and her height above the levelled ground at any time, t, is given as

H(t) = -0.6cos⁡(2π/2.5)t + 1.5

What is t when H = 1.2 m

1.2 = -0.6cos⁡(2π/2.5)t + 1.5

0.6cos⁡(2π/2.5)t = 1.2 - 1.5 = -0.3

Cos (2π/2.5)t = (0.3/0.6) = 0.5

Note that in radians,

Cos (π/3) = 0.5

This is the first time, the second time that cos θ = 0.5 is in the fourth quadrant,

Cos (5π/3) = 0.5

So,

Cos (2π/2.5)t = Cos (5π/3)

(2π/2.5)t = (5π/3)

(2/2.5) × t = (5/3)

t = (5/3) × (2.5/2) = 2.0833333 = 2.08 s to the neareast hundredth of a second.

Hope this Helps!!!

4 0
3 years ago
Whats the answer for taking its square root?<img src="https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%2068" id="TexFormula1" title="y^
Reil [10]

Answer:

y=\pm 2\sqrt{17}

Step-by-step explanation:

y=\pm \sqrt{68} \\ \\ y=\pm 2\sqrt{17}

4 0
1 year ago
Line L pases through Sand R. Determine the slope of L.
mart [117]

Answer:

hi you answer should be 5/3

Step-by-step explanation:

Hope this helps!

8 0
2 years ago
Write the six step in division
joja [24]

Answer:

Divide the tens column dividend by the divisor. Multiply the divisor by the quotient in the tens place column. Subtract the product from the divisor

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • Drawn<br> two arrays that represent 12
    7·1 answer
  • Find the yy-intercept of the equation y=(x−5)2+2.
    8·1 answer
  • This is #16. Now #17 says “For question #16, find a value of x that makes lines u and v intersect.” Help me.
    12·1 answer
  • Which expression is equivalent to StartRoot StartFraction 8 Over x Superscript 6 Baseline EndFraction EndRoot? Assume x Greater-
    15·1 answer
  • What is 5.6=?HELP ME!
    15·1 answer
  • White 15/45 in simplest form
    5·2 answers
  • Use (&lt;, &gt;, =) to compare 2⁄3 and 3⁄4.
    12·1 answer
  • Solve 8 Divided by 0
    13·1 answer
  • Which property is used to simplify 45and + 3 (25x+75Y) to 5y + 65x?
    5·1 answer
  • Find the volume of the solid<br><br><br><br> The problem is in the picture!!!!!!!!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!