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
Write an equation for the graph below in slope-intercept form:
Zanzabum

Answer: y<1x-2

Step-by-step explanation:

Find some coordinates on the line to write a slope intercept form equation for the line and turn it into inequality.

First we need to find the slope and the y-intercept. The y intercept is when x is 0 and as we can see it  already indicates that the y intercept is -2 .

(0,-2)

(2,0)   Use these points o the find the slope.

0- 2 = -2

-2 -0 = -2

-2/-2 = 1   The slope is one so the equation will be y = 1x - 2   But since this is not an inequality we have to change the equal to sign to an inequality sign.

Looking at the line, it is a dashed line so the inequality sign will be > or <  

The painted side of the graph represents the solutions of the graph  and that is all underneath the graph so the inequality will be   y < 1x-2

8 0
3 years ago
Use the explicit
Leno4ka [110]

Answer:913

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
if it asks for scale factor does that mean i’m supposed to write a ratio? Can someone solve and explain these for me i’m so conf
STatiana [176]
Yes scale factor means ratio. The height of the smaller pyramid to the larger pyramid in ratio form is 8:24 which simplifies to 1:3. The ratio of its areas is the scale factor squared, so 1^2:3^2=1:9. Since the surface area of the smaller pyramid is 124, the surface area of the larger pyramid must be 124x9. The ratio of volumes is the scale factor cubed, so 1^3:3^3=1:27. If the volume of the larger pyramid is 648, then the volume of the smaller pyramid is 1/27 of that, which equals 24.
8 0
3 years ago
700 students attend Ridgewood Junior High School. 5% of students bring tlieir lunch
Butoxors [25]

Answer:

35

Step-by-step explanation:

bc if u change the 5% into .05 than u multiply it to get 35 sorry if I am wrong or to late

6 0
3 years ago
According to the U.S. Department of Agriculture in 2011, the cost of raising a child from birth to eighteen years of age is appr
My name is Ann [436]

Answer:

$234,900

Step-by-step explanation:

Quick Search on the internet

3 0
1 year ago
Read 2 more answers
Other questions:
  • Please help me with 13 12 10 9 8 6 BONUS:7 44 POINTS!!!
    10·2 answers
  • Which of the following is equivalent to the equation 2(x-3) 5(x+1)
    5·1 answer
  • I need the quadratic formula.​
    10·2 answers
  • peter ​says, "If you subtract 11 from my number and multiply the difference by -2​, the result is -26." What is Peter's number?
    5·2 answers
  • The table shows equivalent ratios for converting from the United States dollar (USD) to the Canadian dollar (CAD). What is the C
    13·2 answers
  • A boy stands 1 meter away from a lamppost. He is 1.8 meters tall and casts a shadow 2 meters long in the light from the lamp. Ho
    6·2 answers
  • Can someone tell me what “increase s by 2s” is
    15·2 answers
  • How much interest will Henry save if he finances the vehicle over 36 months instead?
    7·1 answer
  • This is a question from my sibling's math class.
    14·2 answers
  • If you sell $1000 worth of popcorn, then your Boy Scout dues are free. Ethan sold $1000 worth of popcorn. Conclusion: Ethan's Bo
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!