All categories

2 years ago

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]2 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

Plz help! The product of three consecutive natural numbers is 336. What are those numbers?

bekas [8.4K]

Answer:

2x2x2x2x3x7,This is because all of that sum equals the total of

Step-by-step explanation:

2x2x2x2x3x7

8 0

2 years ago

How do you divde monomials?

Alexeev081 [22]

Divide the numerical coefficients and write the quotation in simplest form

8 0

2 years ago

Read 2 more answers

Which statement is a correct interpretation of the vertical line test?

Veseljchak [2.6K]

Vertical line is a way to determine whether a functin is a function or not.

5 0

2 years ago

Read 2 more answers

Andrew is riding his bike. He biked a distance of 14 miles at a rate of 7 miles per hour. Using the distance formula, d = rt, so

rusak2 [61]

The computation shows that the time taken is 120 minutes.

<h3>How to illustrate the information?</h3>

From the information, Andrew is riding his bike and he biked a distance of 14 miles at a rate of 7 miles per hour.

Therefore, time taken for 14 miles will be:

= 14/7

= 2 hours

= 2 × 60 = 120 minutes

The time taken is 120 minutes.

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

3 0

1 year ago

Answer as many as you can please (write in slope-intercept form)

RoseWind [281]

Answer: See below

Step-by-step explanation:

For the first one, we are already given our slope. All we need to do is find the y-intercept, b.

y=-2x+b

6=-2(-3)+b

6=6+b

b=0

The slope-intercept form is y=-2x.

For the second one, we need to first find the slope using $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ .

$m=\frac{1-13}{3-(-6)} =\frac{-12}{9}$

Now that we have our slope, we can plug it into our slope-intercept form to solve for b.

$y=-\frac{12}{9} x+b$

$3=-\frac{12}{9}(1)+b$

$-\frac{9}{4} =b$

The slope-intercept form is $y=-\frac{12}{9} -\frac{9}{4}$ .

For the third one, we are already given the slope, so all we have to do is find b.

$y=-\frac{1}{2}x +b$

$-7=-\frac{1}{2} (-4)+b$

$-7=2+b$

$-9=b$

The slope-intercept form is $y=-\frac{1}{2} x-9$ .

For the last one, we need to first find the slope using $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ .

$m=\frac{-8-2}{3-1}=\frac{-10}{2} =-5$

Now that we have our slope, we can plug it into our slope-intercept form and find b.

$y=-5x+b$

$2=-5(1)+b$

$2=-5+b$

$7=b$

Our slope-intercept form is $y=-5x+7$ .

4 0

3 years ago