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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

           

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The sum of a number and 4 is equal to -43. Find the number
Artist 52 [7]

Answer:

the number is -47..

Step-by-step explanation:

let the number be'x'

  • x+4= -43
  • x= -43-4
  • x= -47

hope it helps.

<h2>stay safe healthy and happy.</h2>
4 0
3 years ago
Read 2 more answers
Why is the remainder always less than the divisor
anastassius [24]
The remainder is always less than the divisor because if the remainder was more than the divisor then you would have a totally different answer. If the remainder was more than the divisor than you know your answers wrong.
4 0
3 years ago
What is the slope of the line that passes through the points (9, -1) and (4, -11)?
mixas84 [53]

Answer:

2

Step-by-step explanation:

We have two points so we can find the slope

m = ( y2-y1)/(x2-x1)

    = ( -11 - -1)/( 4 -9)

    = (-11+1)/( 4-9)

    -10/ -5

   = 2

4 0
2 years ago
11. When you multiply two decimals less than 1, how does the product compare to the factors?
ANEK [815]

Answer:

The product is usually smaller than the two numbers multiplied

Step-by-step explanation:

When we multiply two decimals less than one, it is a certainty that the result of the multiplication would be less than the two decimals that were multiplied. An example is the multiplication of the decimals below;

0.958 * 0.325

which equals 0.31135

We can see from the example above that the result of the multiplication of the two decimals that are less than one, results in a product that is less than the factors that were multiplied.

5 0
3 years ago
Check all of the expressions that are equal to the one below.
Aloiza [94]
(7-11) • (5) = -20

A. (5) • 7 + (5) • (-11)
↳ 35 + (-55)
↳ 35 - 55 = -20

B. -(-7+11) • (5)
↳ -4 • 5 = -20

C. (5) • 7 - (5) • 11
↳ 35 - 55 = -20

D. (7+11) • (5)
↳ 18 • 5 = 90

A B & C are correct
4 0
3 years ago
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