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
trapecia [35]
3 years ago
8

Given cos ⁡ ( θ ) = 5/6 , then sin ⁡ ( θ ) = a/b . Determine the values of a and b.

Mathematics
1 answer:
slega [8]3 years ago
3 0

Answer:

a = √11 and b = 6

Step-by-step explanation:

Refer to attached picture for reference

for an right triangle with angle θ

we are given

cos θ = 5/6 = length of adjacent side / length of hypotenuse

hence

adjacent length = 5 units

hypotenuse length = 6 units

the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:

hypotenuse ² = adjacent ² + opposite²   (rearrange)

opposite ² = hypotenuse ² - adjacent ²

opposite ² = 6² - 5²

opposite = √ (6²-5²) = √11

sin θ = opposite length / hypotenuse  (substitute values above)

sin θ = √11 / 6

hence a = √11 and b = 6

You might be interested in
Use average rates of change to determine if the function in the table is Linear or Non-linear.
nevsk [136]

We have been given a table of values of a function. We are asked to determine whether the given function is linear or nonlinear.

We know that a function is linear when its rate of change (slope) is constant.

Let us find slope for each of the given points using slope formula.

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-3-0}{4-1}=\frac{-3}{3}=-1

Similarly, we will find the slopes using other given coordinates.  

m=\frac{-6-(-3)}{7-4}=\frac{-6+3}{3}=\frac{-3}{3}=-1

m=\frac{-9-(-6)}{10-7}=\frac{-9+6}{3}=\frac{-3}{3}=-1

Since the rate of change for each set of points is -1, so the rate of change is constant.

Therefore, the given function is linear.

3 0
3 years ago
HELPPP <br> If Julie makes $20,000 a year, how much will she make in a day?
NNADVOKAT [17]
I’m not sure I would help you if knew
7 0
2 years ago
What is the answer to -6n^2 - 5n - 7 = -8
soldi70 [24.7K]

Answer:

n = \frac{1}{3} , n = \frac{1}{2}

Step-by-step explanation:

6n² - 5n - 7 = - 8 ( add 8 to both sides )

6n² - 5n + 1 = 0 ← in standard form

Consider the product of the factors of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term

product = 6 × 1 = 6 and sum = - 5

The factors are - 3 and - 2

Use these factors to split the n- term

6n² - 3n - 2n + 1 = 0 ( factor the first/second and third/fourth terms )

3n(2n - 1) - 1(2n - 1) = 0 ← factor out (2n - 1) from each term

(2n - 1)(3n - 1) = 0 ← in factored form

Equate each factor to zero and solve for n

3n - 1 = 0 ⇒ 3n = 1 ⇒ n = \frac{1}{3}

2n - 1 = 0 ⇒ 2n = 1 ⇒ n = \frac{1}{2}

7 0
3 years ago
Aria drank 500 milliliters of water after her run. Her best friend, Andrea, drank 0.75 liter of water. Who drank more?
Paul [167]
To answer this item, let us convert first one of the given dimension such that both numbers will take only the same units for easier comparison. It should be noted that every liter (L) is consists of 1000 mL. 

Aria: (500 mL)(1 L/1000 mL) = 0.5 L
Andrea: 0.75 L

Since, 0.75 L is higher compared to 0.5L, the answer to the item is Andrea. 
8 0
3 years ago
What happens to infrared radiation released by the Earth if there is an increased level of carbon dioxide in the atmosphere? (1
motikmotik

Answer: It is absorbed and heats the atmosphere.​

Step-by-step explanation:  it's absorbed and emitted back toward Earth's surface.

5 0
2 years ago
Other questions:
  • How do I do the rest? Am I even doing it right
    11·2 answers
  • Someone’s mother has four sons. North, South and East. What is the name of the fourth son. Private message me the name of the fo
    15·2 answers
  • Write the expression <br> 6 less 7 times a number
    10·2 answers
  • There are 30 flavors and you can mix up to 3 of them. How many flavor possibilities are there? You can't mix the same flavors mo
    13·1 answer
  • 8 1/4x5 1/2what is the answer to this
    10·2 answers
  • Whats 13 times 13 first one right gets 10 points
    9·2 answers
  • Which of the following is a solution of x2 − 6x = –22?
    7·2 answers
  • Fred Has A bag Of Sweets:
    6·1 answer
  • In Raphael's class there are 14 boys and 10 girls. Select whether each statement is true or false.
    8·2 answers
  • HEEELLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!