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
stealth61 [152]
2 years ago
9

Solve the equation on the interval [0,2pi] 5sec(x)+7=-3

Mathematics
2 answers:
vovangra [49]2 years ago
8 0

Answer:

Hello,

x\in \bigg\{\dfrac{2\pi}{3} ,\dfrac{4\pi}{3}\bigg\}\\

Step-by-step explanation:

5*sec(x)+7=-3\\\\sec(x)=\dfrac{-10}{5} \\\\\dfrac{1}{cos(x)} =-2\\\\cos(x)=-\dfrac{1}{2} \\\\x=120^o\ or\ x=240^o\\

Alex17521 [72]2 years ago
3 0

Answer:

\sf \boxed{\sf x = \dfrac{2\pi}{3},\dfrac{4\pi}{3}}

Step-by-step explanation:

A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]

The given equation is ,

\sf\longrightarrow 5 sec\  x +7 = -3

Add -7 to both sides ,

\sf\longrightarrow 5sec\ x = -10

Divide both sides by 5 ,

\sf\longrightarrow sec \ x =\dfrac{-10}{5}

Simplify ,

\sf\longrightarrow sec \ x =-2

Now solve for x ,

\sf\longrightarrow x = sec^{-1}(-2)

Simplify ,

\sf\longrightarrow x = \dfrac{2\pi}{3}

The secant function is <u>negative in the second and third quadrants. </u> Subtracting the reference angle from <u>2</u><u>π</u><u> </u> to find the solution in the third quadrant to find the solution second solution.

\sf\longrightarrow x = 2\pi -\dfrac{2\pi}{3}

Simplify ,

\sf\longrightarrow x = \dfrac{4\pi}{3}

Now here the period of sec x is <u>2</u><u>π</u> . Therefore ,

\sf\longrightarrow x = \dfrac{2\pi}{3} +2\pi n , \dfrac{4\pi}{3}+2\pi n , \textsf{ for any integer n } .

Therefore all the possible solutions are ,

\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{2\pi}{3},\dfrac{4\pi}{3}}}

<u>Hence</u><u> the</u><u> </u><u>required</u><u> </u><u>answer</u><u> </u><u>is </u><u>2</u><u>π</u><u>/</u><u>3 </u><u>and </u><u>4</u><u>π</u><u>/</u><u>3.</u>

You might be interested in
I don't understand how to solve this please help
I am Lyosha [343]
Area=pi x radius squared so (3.14)(10)squared = 314
3 0
3 years ago
Read 2 more answers
-10x - 135 = 117 + 2x<br> A. 25<br> B. -18<br> C. -21<br> D. 22 <br> Helps pls
Lina20 [59]

Answer:

C

Step-by-step explanation:

Add 10x to both sides:

-10x - 135 = 117 + 2x

-10x - 135 + 10x = 117 + 2x + 10x

-135 = 117 + 12x

Subtract 117 from both sides:

-135 - 117 = 117 + 12x - 117

-252 = 12x

Divide both sides by 12:

\frac{-252}{12} = \frac{12x}{12}

-21 = x

So the answer is C.

Hope this helps!

6 0
2 years ago
Read 2 more answers
Fairview High School has a total of 92 boys and girls who play sports. If the number of boys is 17 more than twice the number of
MaRussiya [10]
Girls = x
boys = y

y = 92 - x
y = 17 + 2x

y = 92 - x
-y= -17 - 2x
0 = 75 - 3x
3x = 75
x = 25

25 girls play sports at the school
y = 92 - 25
y = 67

67 boys play sports at the school


8 0
3 years ago
Can anyone help me with this?
Nostrana [21]
Find the area but calculating it
7 0
2 years ago
Read 2 more answers
Which is the slope of the line with the equation of y=-4x that passes through (3,1)?
makkiz [27]
The slope is -4. The slope is always determined by the coefficient of the x variable when in the form stated by the question. The point given is arbitrary to find the slope.
6 0
3 years ago
Other questions:
  • Please help i don't understand it
    15·1 answer
  • An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 1.6 ft. S
    9·1 answer
  • What is the value of y?
    6·1 answer
  • Joe burns 41 calories in of a minute riding his bike. What is Joe's unit rate?
    6·1 answer
  • Is the square root of 3 rational or irrational
    10·1 answer
  • Linear regression describes the extent to which _______ predicts ________. X; Y the predictor variable; the criterion variable t
    8·1 answer
  • The sum of two numbers 94. their diffirence is 12
    7·2 answers
  • 6x2y − 3xy − 24xy2 + 12y2
    6·2 answers
  • Solve for B: Ax + By = EF <br> HURRY WILL GIVE BRAINLIEST
    11·1 answer
  • Look at the images and answer the question: What is the length of GW?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!