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
Juliette [100K]
3 years ago
9

Find the angles between -pi and pi that satisfy: (−√3) sin(v)+cos(v)=√3

Mathematics
1 answer:
MAXImum [283]3 years ago
3 0

Observe that

\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v

In the original equation, divide both sides by \dfrac12:

-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2

\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2

Next,

\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi

where n is any integer. Then

\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi

Fix n=0 to ensure -\pi, so that

v=-\dfrac\pi6,v=-\dfrac\pi2

You might be interested in
The length of a rectangle is four times its width.
mixer [17]

Let width be x

  • length=4x

ATQ

\\ \sf\longmapsto 2(x+4x)=70

\\ \sf\longmapsto 5x=35

\\ \sf\longmapsto x=7

  • Width=7ft
  • Length=7(4)=28ft
3 0
2 years ago
Read 2 more answers
Can someone help me figure out this
QveST [7]

Answer:

YES

Step-by-step explanation:

The criterion for formation of a triangle is that the sum of any 2 sides should be greater than or equal to the third side

So, we will test it for all 3 sides

7.4 + 12.5 ≥ 19.9

TRUE

12.5 + 19.9 ≥ 7.4

TRUE

7.4 + 19.9 ≥ 12.5

TRUE

Therefore, the segments with the sides: 7.4 , 12.5 and 19.9 do form a triangle

4 0
3 years ago
Read 2 more answers
How many eggs in a dozen
Over [174]

Answer:

Step-by-step explanation:

a dozen is 12, whether its eggs or anything else (except a bakers dozen)

4 0
2 years ago
Read 2 more answers
Is it possible to have a negative value for sin but a positive value for tangent
bonufazy [111]

Answer:

Yes

Step-by-step explanation:

Tan = sin / cos

If sin is negative, ans cos is negative, then tangent is positive.

Tan= (-)/(-) = (+)

7 0
3 years ago
What is the value of x?<br> Enter your answer in the box.
loris [4]

Answer:

35

Step-by-step explanation:

Since all the angles are the same in this triangle, all the sides should be the same too.

Hence, 3x - 5 = 4x - 30

5 + -1x = -30

-1x = -35

x = 35

Hope this helped!

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which statements are true about tessellations?
    8·1 answer
  • 5.8 cm ___ 580 mm<br><br> A : &gt; <br><br> B : &lt; <br><br> C : =
    11·2 answers
  • Which expression is equivalent to 18x + 45?
    12·2 answers
  • A child is to receive a dose of 0.5 teaspoon of medicine every 6 hours. If the bottle contains 60 doses, how many days will the
    12·1 answer
  • A vehicle uses 1 gallons of gasoline to travel 13 miles. At this rate, how many mile
    13·1 answer
  • Solve for x. x - 8 = -10​
    10·1 answer
  • Please help ASAP!!!!!! The first figure is dilated to form the second figure
    12·1 answer
  • Alyssa is planning to have a lemonade stand. Alyssa and her mom make 165 ounces of lemonade. If Alyssa fills each cup equally wi
    6·1 answer
  • 7cm<br> 9cm<br> 4cm<br> 4cm<br> Find the area
    6·1 answer
  • Use distributive property to rewrite the expression 3x(x+4)​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!