What is the value of cos given that (-2, 9) is a point on the terminal side of ?

Answer: a) cos = [tex]\frac{-2\sqrt{85} }{85}[/tex]Step-by-step explanation: Step(i):-Given point ( x , y ) = ( - 2 , 3 )We know that the polar co-ordinates x = r cos and y = r sin where [tex]r = \sqrt{x^{2} +y^{2} }[/tex] [tex]r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}[/tex]Step(ii):- x = r cos cos [tex]= \frac{x}{r}[/tex] cos = [tex]\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }[/tex] cos = [tex]\frac{-2\sqrt{85} }{85}[/tex]

Mathematics High School

What is the value of cos θ given that (-2, 9) is a point on the terminal side of θ?

What Is The Value Of Cos Given That (-2, 9) Is A Point On The Terminal Side Of ?

Answers

Answer 1

Answer:

a) cosθ = [tex]\frac{-2\sqrt{85} }{85}[/tex]

Step-by-step explanation:

Step(i):-

Given point ( x , y ) = ( - 2 , 3 )

We know that the polar co-ordinates

x = r cos θ and y = r sinθ

where [tex]r = \sqrt{x^{2} +y^{2} }[/tex]

[tex]r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}[/tex]

Step(ii):-

x = r cos θ

cosθ [tex]= \frac{x}{r}[/tex]

cosθ = [tex]\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }[/tex]

cosθ = [tex]\frac{-2\sqrt{85} }{85}[/tex]

Related Questions

2) Angelina is deciding which bank would give her the

best simple interest rate on a $300 deposit. One bank

says that she will have $320 in her account if she leaves

the principal for two years. Is this enough information

for Angelina to find the interest rate? Explain.

HELPPPP

Answers

Answer:

3.33%

Step-by-step explanation:

Given that :

Final amount A= 320

Principal P = 300

Time (t) = 2 years

Yes, the information is enough to obtain the interest rate :

Using the relation :

A = P(1 + rt)

r = interest rate

320 = 300(1 + r*2)

320 = 300(1 + 2r)

320/300 = 1 + 2r

1.0666666 = 1 + 2r

1.0666666 - 1 = 2r

0.0666666 = 2r

r = 0.0666666 / 2

r = 0.0333333

(0.0333333) * 100% = 3.33%

Based on the information given the interest rate is 53.33%.

Interest rate:

Amount= Principal× Interest rate ×Time/100

Let r represent the interest rate

Hence:

320 = 300×r×2 years/100

320×100/300×2=r

r=320/3×2

r=160/3

r=53.33 or 53 1/3

Inconclusion the interest rate is 53.33%.

Learn more about interest rate here:https://brainly.com/question/25545513

expression for the width and the length of 6 x ^ 2 - 11x - 10

Answers

Area = (length)(width)

6x2 + 11x + 5 = (length)(x + 1)

(x + 1)(6x + 5) = (length)(x + 1)

Divide both sides by x + 1 to get : length = 6x + 5

Lea earned $24 babysitting. She spent ⅔ of that amount on a gift for her bestie, ¼ on snacks. What fraction of her earning is left? How much money does she have left?

Answers

Answer:

5/12, $10

Step-by-step explanation:

Lea earned $24 babysitting. She spent ⅔ of that amount on a gift for her bestie, ¼ on snacks. What fraction of her earning is left? How much money does she have left?

Let the total amount earned be 1

Given

Amount on snacks = ¼

Amount on babysitting = ⅔

Required

Fraction left

Fraction left = Total -(snacks+babysitting)

Fraction left = 1-(1/4+2/3)

Fraction left = 1-(3+4/12)

Fraction left = 1-7/12

Fraction left = 5/12

Amount of money she has left = 5/12 × 24 = 5×2 = $10

Hence she has $10 left

help pls, solve what u can

Answers

Answer:

1. V≈1244.07

2. V≈54286.72

3.V≈23816.41

4. V≈254.47

5. V≈4247.43

6. V≈21714.69

7. V≈4712.39

Step-by-step explanation:

use the formula V=πr^2h

The volume of the given cylinders is 1. V≈1244.07 2. V≈54286.72 3. V≈23816.41 4. V≈254.47 5. V≈4247.43 6. V≈21714.69 7. V≈4712.39.

What is the volume of a cylinder?

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2} h[/tex]

a) The height of the cylinder is given as 11 in and the radius is 6 in.