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
Naddika [18.5K]
3 years ago
12

Evaluate the six trigonometric functions of the angle 0.

Mathematics
1 answer:
Arturiano [62]3 years ago
8 0

Given:

Right triangle

To find:

The six trigonometric functions of θ

Solution:

Hypotenuse = 18

Adjacent side to θ = 10

Opposite side to θ = ?

Using Pythagoras theorem:

\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2

18^2 =10^2+\text{opposite}^2

324=100+\text{opposite}^2

Subtract 100 from both sides.

224=\text{opposite}^2

Taking square root on both sides.

4\sqrt{14}=\text{opposite}

Using trigonometric ratio formula:

$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}

$\sin\theta =\frac{4\sqrt{14} }{18}

$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}

$\csc\theta =\frac{18}{4\sqrt{14} }

$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}

$\cos \theta=\frac{10}{18}

$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}

$\sec \theta=\frac{18 }{10}

$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}

$\tan \theta=\frac{4\sqrt{14} }{10}

$\cot \theta=\frac{\text { adjacent side }}{\text { opposite side }}

$\cot \theta=\frac{10}{4\sqrt{14} }

You might be interested in
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high
Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0
3 years ago
MATH hw help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
dolphi86 [110]
"Bucket method"
.. (4)*(14%) + (x)*(8%) = (4 +x)*(10%) . . . . . liters and % are in each "bucket"
.. 56 +8x = 40 +10x . . . . . multiply by 100, eliminate parentheses
.. 16 = 2x . . . . . . . . . . . . . . add -40-8x, then divide by 2
.. 8 = x

8 liters of 8% lemonade should be added to make the mixture 10% lemon juice.
4 0
3 years ago
Factor this expression completely, then place the factors in the proper location on the grid. 9x2 - y2
andreev551 [17]

Answer:

{ \tt{ {9x}^{2} -  {y}^{2}  }} \\  = { \tt{( {3x)}^{2} -  {y}^{2}  }} \\  = { \tt{(3x - y)(3x + y)}}

6 0
2 years ago
Double a number decreased by 4
Wittaler [7]

Answer:

2x-5 if u want u can substitute any other variables and constant

3 0
2 years ago
Read 2 more answers
Janet wanted to determine her average phone call length over 90 days. She collected the phone bills and randomly picked ten entr
muminat

oops sorry wrong question. sorry if I confused anyone :(

3 0
2 years ago
Other questions:
  • Melissa bought 42 pine seedlings and 30 juniper seedlings
    7·1 answer
  • Can someone help with this math question
    14·1 answer
  • A bag contains only red, green, brown and yellow marbles.
    13·1 answer
  • The second question please!
    14·1 answer
  • Calculators were purchased at $70 per dozen and sold at $20 for three calculators. What is the profit on six dozen calculators?
    7·1 answer
  • Y= 8x - 9 y = 8x +1 A. Perpendicular B. Neither C. Parallel
    7·1 answer
  • 1. The average Third grade student can read 60 words in 5 minutes What is the average reading rate per minute?​
    15·2 answers
  • The surface area of a cone with radius r units and slant height s units is shown below: Surface area = 3.14(rs + r2) Part A: If
    8·1 answer
  • Question is in the photo!
    9·2 answers
  • A racerunner is 26. 7 cm long. How much less than a meter is this?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!