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
Ede4ka [16]
3 years ago
11

Find the exact value of sec theta if csc theta = -4/3 and the terminal side of theta lies in quadrant III

Mathematics
1 answer:
GREYUIT [131]3 years ago
3 0

Answer:

-4 sqrt(7)/7

Step-by-step explanation:

csc theta = -4/3

csc theta = hypotenuse / opposite side

hypotenuse = 4  

opposite  = 3

Using the pythagorean theorem

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9+b^2 = 16

b^2 = 16-9

b^2 = 7

Taking the square root

sqrt(b^2) = sqrt(7)

b = sqrt(7)

We are in the third quadrant so only tan  and cot are positive

that means the x and y values are "negative"  so a = -3 and b = - sqrt(7)

sec theta = hypotenuse / adjacent

                = 4/ - sqrt(7)

rationalizing  

                   -4 sqrt(7)/ sqrt(7)* sqrt(7)

                = -4 sqrt(7)/7

           

You might be interested in
F(x) = 3x-1 and g(x)=2x^2
Law Incorporation [45]

Answer:

See below

Step-by-step explanation:

a.  here you are to multiply the two functions together:

(3x-1)(2x^{2} )=6x^{3}-2x^{2}

b.  here you are to subtract g from f:

(3x-1)-(2x^{2})=-2x^{2}+3x-1

c.  here you are to compose g into f.  In other words, pick up the whole g function and plug it into f wherever you see an x:

3(2x^{2} )-1=6x^{2} -1

d.  here you are compose f into g.  In other words, pick up the whole f function and plug it into g wherever you see an x:

2(3x-1)^2

You now have to FOIL out the (3x-1) like so:

2[(3x-1)(3x-1)]

which gives you

2(9x^{2} -6x+1)

Distribute in the 2 and you'll end up with the answer:

18x^{2} -12x+2

3 0
3 years ago
Find the measure of each angle in the triangle.
VMariaS [17]

Answer:

C. 26°, 64°, 90°

Step-by-step explanation:

7 0
3 years ago
Given a line segment that contains the points A,B, & C in order, if AB = x + 12, and BC = 2x - 4, and AC = 26, find x.
Troyanec [42]

Answer:

x = 6

Step-by-step explanation:

If A, B and C lies on a straight line in order, then;

AB+BC = AC

x+12+2x-4 = 26

x+2x+12-4 =26

3x+8 = 26

3x = 26-8

3x = 18

x = 18/3

x = 6

Hence the value of x is 6

4 0
3 years ago
Any one help please
zvonat [6]

Answer:

1: male + female \leq 30

2: 140 + 25x \geq 550

Step-by-step explanation:

8 0
3 years ago
Write the equation of the line in slope-intercept form.
Natasha_Volkova [10]

Answer:

y=-1/2x-2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • A shop recorded total sales of $2,000 on Monday. On Tuesday, its sales fell by 10%. On Wednesday, sales fell by another 20% comp
    6·2 answers
  • Sam subtracted 5 from the quotient of a number and 3. Write an algebraic expression to represent the operations that Sam preform
    14·1 answer
  • I need help with both of these you’re supposed to solve by graphing?
    15·1 answer
  • The base radius of an ice cream cone is 3.5 cm and the slant height is 6.5 cm. What is the capacity of the ice cream cone and it
    15·2 answers
  • Premium steak costs $18 per pound; how much steak cost per ounce ?
    9·1 answer
  • We say that an integer a is a type 0 integer if there exists an integer n such that a = 3n. An integer a is a type 1 integer if
    11·2 answers
  • Graph y=-x+4 and -4x+2y=2
    9·1 answer
  • What is the answer? <br> Plzz answer fast! <br> I’ll put you in brainliest.
    8·1 answer
  • Square A is smaller than Square B. Square B is smaller than Square C.
    14·1 answer
  • Ryan has 4 cups of grape juice, and Kelsey has 7 cups of lemonade. They want to combine what they have to make punch. How many 1
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!