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
Which table corresponds to the graph of the function below?
sweet-ann [11.9K]
B corresponds to the graph.
8 0
2 years ago
Read 2 more answers
Part A. Let $f(x) = x^4-3x^2 + 2$ and $g(x) = 2x^4 - 6x^2 + 2x -1$. Let $a$ be a constant. What is the largest possible degree o
Varvara68 [4.7K]

Answer:

  A.  4

  B.  1

Step-by-step explanation:

The degree of a one-variable polynomial is the largest exponent of the variable.

__

<h3>A.</h3>

For f(x) = x^4 -3x^2 +2 and g(x) = 2x^4 -6x^2 +2x -1, the sum f(x) +a·g(x) will be ...

  (x^4 -3x^2 +2) +a(2x^4 -6x^2 +2x -1)

  = (1 +2a)x^4 +(-3-6a)x^2 +2ax -a

The term with the largest exponent is (1 +2a)x^4, which has degree 4. This term will be non-zero for a ≠ -1/2.

The largest possible degree of f+ag is 4.

__

<h3>B.</h3>

The polynomial sum is ...

  f+bg = (1 +2b)x^4 +(-3-6b)x^2 +2bx -b

When b = -1/2, the first two terms disappear and the sum becomes ...

  f+bg = -x +1/2 . . . . . . a polynomial of degree 1

The smallest possible degree of f+bg is 1.

5 0
2 years ago
Out of 18 cookies, 1/3 are chocolate chip. How many of the cookies are chocolate chip?
ivann1987 [24]

Answer:

6

Step-by-step explanation:

that´s easy its basically dividing 3 by 18 which is 6

6 0
2 years ago
Plz help me answer this
Verizon [17]
If 60% of the painters is 12, then 10% of the painters is 2, and therefore there are 20 painters.
8 0
3 years ago
Read 2 more answers
Reasonable or unreasonable 9/10 - 2/5 = 1 3/10
amid [387]
It's wrong so unreasonable because 2/5 is 4/10 so 9/10 - 4/10 is 5/10 which is a 1/2
4 0
3 years ago
Other questions:
  • Someone help me please
    7·1 answer
  • Identify the type of sequence 1/10, 3/20, 5/30, 7/40...
    14·1 answer
  • What is the reciprocal of the number 2/7 ?
    13·1 answer
  • PLEASE HELP ME
    5·1 answer
  • Please help! 30 points!
    14·2 answers
  • Find the distance between (-1,4) and (5,7).
    9·1 answer
  • What is the answer to 2 4/5+5 2/3 in simplified form
    12·1 answer
  • Students taking an online english test are randomly assigned 3 questions out of a set of 9 different questions. How many differe
    12·1 answer
  • PLEASE HELP ME:<br><br> Find the perimeter of the figure. Round to the nearest tenth.
    12·1 answer
  • I NEED HELP PLEASE! ITS DUE TOMORROW!! THANKS!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!