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
daser333 [38]
3 years ago
9

Find the exact value of cos(sin^-1(-5/13))

Mathematics
1 answer:
son4ous [18]3 years ago
8 0

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

You might be interested in
if 99 certons of milk was sold and 45 of them were regular flavor what is the ratio of chocolate milk sold to regular milk sold+
andreyandreev [35.5K]
Well 99 cartons sold, and 45/99 were normal
therefore 99-45 = 54
the ratio is 54:45 if they ask for chocolate to normal
wording of the question is crucial
I'm not sure if you can cancel the ration down to 6:5, you probably can


7 0
3 years ago
The yummy Ice cream company wants to package ice cream in cylindrical containers that have a volume of 5453 cubic centimeters. T
Lina20 [59]
The radius of the base of the container:
20/(2*3.14)=3.18cm
Area of the base:
3.14*3.18*3.18=31.8cm square
The toll of the container :
5453/31.8
=171.5cm
6 0
3 years ago
Please help me with pythagoras.
lana [24]

Answer:

(q)

cb \:  =  \sqrt{4 {}^{2}  +  {3}^{2} }

cb = 5

q =  \sqrt{ {13}^{2}  -  {5}^{2} }

q = 12

(r)

cb = \sqrt{ {13}^{2} -  {5}^{2}  }

cb = 12

r =  \sqrt{12 {}^{2} - 5 {}^{2}  }

r =  \sqrt{119}

r = 10.91

(s)

ab =  \sqrt{20 {}^{2}  - 16 {}^{2} }

ab = 12

s =  \sqrt{12 {}^{2} + 8 {}^{2}  }

s = 4 \sqrt{13}

s = 14.42

Step-by-step explanation:

8 0
3 years ago
HELP!!!!! PLEASE!!!!!
emmainna [20.7K]

Answer:

4

Step-by-step explanation:

It's a pythagorean triple

8 0
3 years ago
Read 2 more answers
What is the diameter of a hemisphere with a volume of 5403 ft", to the nearest tenth<br> of a foot?
lubasha [3.4K]

Answer:Volume of a sphere is 4/3πr^3

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What same number goes into both 75 and 25?
    14·1 answer
  • A sector of a circle of radius "r" cm has an area of "A"cm². Express the perimeter of the sector in terms of "r" and "A"
    13·1 answer
  • Stephanie built a box to hold sports equipment. The box is in the shape of a rectangular prism. The
    15·2 answers
  • The digits 1, 2, 3, 4, 5, 6, and 7 are randomly arranged to form a? three-digit number. ? (digits are not? repeated.) find the p
    15·1 answer
  • Need help with this question!
    12·2 answers
  • A man walks 6 kilometers towards south and then he traveled 10 kilometers towards west and then 4 kilometers towards north and t
    11·1 answer
  • Can anyone help with this?
    9·1 answer
  • Sovle the question l-9l + l-1l ​
    7·2 answers
  • In the equation y=3x+15<br> What is the slope and y intercept?
    13·1 answer
  • A line with a slope of 8 passes through the point (1, 8). What is its equation in
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!