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
sdas [7]
3 years ago
12

The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of

θ? Make sure to show all work.

Mathematics
2 answers:
Lilit [14]3 years ago
7 0

Check the picture below.

\bf (\stackrel{a}{1}~,~\stackrel{b}{-1})\qquad \impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c = \sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{1^2+(-1)^2}\implies c=\sqrt{2} \\\\[-0.35em] ~\dotfill

\bf sin(\theta ) \implies \cfrac{\stackrel{opposite}{-1}}{\stackrel{hypotenuse}{\sqrt{2}}}\implies \cfrac{-1}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies -\cfrac{\sqrt{2}}{(\sqrt{2})^2}\implies -\cfrac{\sqrt{2}}{2}

\bf cos(\theta ) \implies \cfrac{\stackrel{adjacent}{1}}{\stackrel{hypotenuse}{\sqrt{2}}}\implies \cfrac{1}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{\sqrt{2}}{(\sqrt{2})^2}\implies \cfrac{\sqrt{2}}{2} \\\\\\ tan(\theta ) = \cfrac{\stackrel{opposite}{-1}}{\stackrel{adjacent}{1}}\implies tan(\theta ) = -1

Pie3 years ago
5 0

Graphing the given point takes us to quadrant 4. Drop a perpendicular to the point (1, -1) and draw a line from the origin to the point. This line is the hypotenuse.

Let h = hypotenuse

(-1)^2 + (1)^2 = h^2

1 + 1 = h^2

2 = h^2

Taking the square root on both sides of the equation we get

sqrt{2} = h

In quadrant 4, only cosine is positive.

sine θ = -1/sqrt{2}

cos θ = 1/sqrt{2}

tan θ = -1/1

tan θ = -1

Did you follow?

You might be interested in
In the table adam recorded the miles he travled each day while traveling from Florida to California. Calculate the average rate
blagie [28]

Hi!

<em>To calculate the rate of change between days 4 and 6, we simply take those points, (4, 1503) and (6, 2196) and use the equation in the picture below:</em>

<em />

Now, when we plug it in the equation, it looks like this:

\frac{2196-1503}{6-4} = \frac{693}{2} = 346.5

Therefore, your answer is 346.5 or, rounded, 347.

<em><u>Meaning, your answer is C</u></em>

<em><u></u></em>

Hope this helps and have a great day! :D

5 0
2 years ago
The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width
blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given  perimeter

perimeter of rectangle = 2 ( length +  width )

=> 30.8 km = 2 ( x + y )  

=>x + y = \frac{30.8}{2}

=> y = 15.4 – x             ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,  

=> length^2 + width^2 = diagonal^2

=> x^2 + y^2 = 11^2

=> x^2 + y^2 = 121

On substituting value of y from (1) in above equation we get

=> x^2 + (15.4-x)^2 = 121

=>x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x   = 121

=> 2x^2-30.8x + 237.16 -121  = 0

=> 2x^2-30.8x + 116.16 = 0

Solving above quadratic equation using quadratic formula

General form of quadratic equation is  

ax^2 +bx +c = 0

And quadratic formula for getting roots of quadratic equation is  

x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}

As equation is 2x^2-30.8x + 116.16 = 0, in our case

a = 2 ,  b = -30.8 and c = 116.16

Calculating roots of the equation we get

x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}

x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{(30.8\pm29.33)}4

x=\frac{(30.8+29.33)}{4}

x=\frac{(30.8-29.33)}{4}

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,  

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

6 0
3 years ago
Help with 5,6,8 please
Ipatiy [6.2K]
5. B, The answer is the only one that is false
6. G, Only reasonable answer
7. D, 3/5 is equivelant to 180/300

Hope this helps :D
4 0
3 years ago
an airline is trying to promote its new Boston to Atlanta flight. the usual price for this flight is $315.00. however the airlin
Veronika [31]

\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 315}}{\left( \cfrac{40}{100} \right)315}\implies 126~\hfill \underset{\textit{after discount}}{\stackrel{315~~ - ~~126}{189}}

8 0
2 years ago
Stephen can deliver 14 newspapers in 20 minutes. How many HOURS will it take him to deliver 131 newspaper
LiRa [457]

Answer:

approx. 3 hours

Step-by-step explanation:

14 newspapers in 20 minutes means he can deliver 42 newspapers an hour.

60/42 = 1.4285 newspapers per minute

131 x 1.4285 = 187.1335 minutes = 3.1188 hours

7 0
2 years ago
Other questions:
  • A jar holds 4 1/4 cups of water . How much is this in fluids ounces? Write your answer as a whole number or a mixed number in si
    15·1 answer
  • Henry, Janon, and Clark are playing a card game. The object of the game is to finish with the most points. The scores at the end
    6·1 answer
  • Rhonda has 3 different color shorts, red, blue, and green ---- and a pair of blue jeans and a pair of white jeans. She randomly
    10·1 answer
  • I would like to know the answer to this question,Distribute and combine Like terms 4 (8x - 2) -44
    8·1 answer
  • Determine the principal value of the function: Arc sin(square root of 3/2)
    11·1 answer
  • 3^x+1 +3^x-1=270<br>Solve for x​
    9·1 answer
  • Please help solve this. (Answer is not 80)
    9·2 answers
  • A box of 15 cookies costs 9$ what is the price of 1 coockie​
    10·1 answer
  • 7.2 x 10^-2 and 3 x 10^-1
    8·1 answer
  • Find the squares of (y+3) ​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!