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
tester [92]
1 year ago
10

Find Sin (BAC+30) 80POINTS

Mathematics
2 answers:
gogolik [260]1 year ago
8 0

sin<BAC

  • P/H
  • 16/20

cos<BAC

  • B/H
  • 12/20

NOw

  • sin(<BAC+30)
  • sin<BAC×cos30+cos<BACsin30
  • 16/20(√3/2)+12/20(1/2)
  • 2/5√3+3/10
Ann [662]1 year ago
3 0

Answer:

\dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}

Step-by-step explanation:

<u>Trigonometric Identities</u>

\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos (\angle BAC)=\dfrac{12}{20}
  • \sin (\angle BAC)=\dfrac{16}{20}

<u>Angles</u>

\sin (30^{\circ})=\dfrac{1}{2}

\cos (30^{\circ})=\dfrac{\sqrt{3}}{2}

Therefore, using the trig identities and ratios:

\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}

You might be interested in
Which is the graph of the equation y-1=2/3(x-3)
Alexxandr [17]

The attachment is the graph of the equation y - 1 = 2 / 3 (x - 3)

4 0
3 years ago
Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis
Tasya [4]
Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5


A.
\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx

B.
sepearte the integrals
\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}

next one
\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}

the last one you can do yourself, it is \frac{50}{3}
the sum is \frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}


so the area under the curve is \frac{233}{3}
6 0
2 years ago
I am not irrational, I am an integer, I am a natural number, and I am a prime number. What number am I?
LuckyWell [14K]

Answer:

I think 1

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
CAN SOMEONE HELP ME PLEASE???
lana66690 [7]

Answer:

Step-by-step explanation: First, you need to write all your data down from least to greatest. Next, count up all the numbers to see how many students. Then you want to find the mean which is average (add then divide). Median is the middle so you will x each number out till you get to the middle, and if the middle is 2 numbers, you find the average of them to find the median. Mode means most often. Range is highest minus lowest. And you can do the next 2.

4 0
3 years ago
Read 2 more answers
Please help with 18 and 19 ASAP ill do brainiac
DanielleElmas [232]

Answer:

18). y = -x

19). y = -2x + 4

3 0
3 years ago
Other questions:
  • W+ 1/2=1/4w + 2 can somebody help me plz
    6·1 answer
  • Hannah rolls two number cubes with the numbers 55536 6 on each what is the probability that she rolled two numbers with an even
    15·1 answer
  • All of the following types of graphs are used to represent numerical data except a . box and whisker pot
    11·1 answer
  • Is the graph a function?
    9·2 answers
  • En un consultorio medico infanfil se consultas mensualmente a 160 pacientes si la razon de cada 8 paciente 5 son niñas A ¿cuanto
    7·1 answer
  • An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate ma
    7·1 answer
  • Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
    15·1 answer
  • Julie drank 4 5 liter of water Monday before going jogging. She drank 2 3 liter of water after her jog. How much water did Julie
    15·1 answer
  • Which of the following pairs shows triangles that are similar but not congruent?
    10·1 answer
  • Identify the property shown - Commutative, Associative, or Identity
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!