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
Sphinxa [80]
3 years ago
8

Simplify the expression. sine of x to the second power minus one divided by cosine of negative x

Mathematics
2 answers:
earnstyle [38]3 years ago
5 0

Answer:

-cos \ x

Step-by-step explanation:

First of all, we must have to understand what is the described expression in the paragraph

"<em>sine of x to the second power minus one divided by cosine of negative x</em>"

In this sentence, we need to identify what are the elements and operations involved in the expression.

In the sentence appears ""to the second power", "minus" and "divided by" (highlighted)

"<em>sine of x </em><em>to the second power</em><em> </em><em>minus</em><em> one </em><em>divided by</em><em> cosine of negative x</em>"

Therefore, the expression must has three operations:

  • "to the second power": refers to exponentiation
  • "minus": refers to a substraction
  • "divided by": refers to a division

Now, we can identify what are the elements: "sine of x", "one" and "cosine of negative x"

  • "sine of x": refers to sin\ x
  • "one": refers to the number one (1)
  • "cosine of negative x": refers to cos (-x)

Therefore, the expression is:

\frac{(sin\ x)^{2}-1}{cos(-x)}

In order to find the simplified expression, we must have to apply these trigonometric identities:

  • (sin\ x)^{2} = sin^{2}x
  • sen\x^{2}x \ +\ cos\x^{2}x=1
  • cos(-x)=cos\ x

Applying the first and third identities, we have:

\frac{(sin\ x)^{2}-1}{cos(-x)}=\frac{sin\x^{2}x-1}{cos\ x}

From the second trigonometric identity, we have:

cos\x^{2}x=\ 1-sin\x^{2}x

Now, multiplying by -1 in both sides:

(-1)(cos\x^{2}x)=(-1)(1-\ sin\x^{2}x)

In the left side, multiplying by -1 the sign of the expression changes:

(-1)(cos\x^{2}x)=-cos\x^{2}x

In the right side, multiplying by -1 changes the order of the substraction:

(-1)(1-\ sin\x^{2}x)=\ sin\x^{2}x-1

Putting all together:

-cos\x^{2}x=\ sin\x^{2}x-1

Now, replacing values we have:

\frac{sin\x^{2}x-1}{cos\ x}=\frac{-cos\x^{2}x}{cos\ x}=-\frac{cos\x^{2}x}{cos\ x}

Finally, the property of the first trigonometric identity (property of exponentiation) can be apply in this case:

-\frac{cos\x^{2}x}{cos\ x}=-\frac{(cos\ x)^{2}}{cos\ x}=-cos\ x

slega [8]3 years ago
4 0

Answer:

the answer is the letter a) -sin x

Step-by-step explanation:

Simplify the expression.

sine of x to the second power minus one divided by cosine of negative x

(1−sin2(x))/(sin(x)−csc(x))

sin2x+cos2x=11−sin2x=cos2x

cos2(x)/(sin(x)−csc(x))csc(x)=1/sin(x)cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))sin2(x)− 1=-cos2(x)cos2(x)/(( -cos2(x))/sin(x))

=-sin(x)

You might be interested in
A submarine let Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier t
Alchen [17]

Answer: the speed of the submarine is 5miles per hour

Step-by-step explanation:

The submarine left Hawaii two hours before the aircraft carrier.

Let x = the speed of the submarine

The aircraft carrier traveled at 25 mph for nine hours.

After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours

Distance travelled = speed × time

Distance travelled by submarine will be 11 × x = 11x miles per hour

Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour

If they are 280 miles apart, this would be their total distance. Therefore,

225 + 11x = 280

11x = 280 - 225 = 55

x = 55/11 = 5miles per hour

8 0
3 years ago
PLZ HELP ASAP DONT SKIP IT AWNSER IT PLZ
Ugo [173]
I think it is friction sorry if I am wrong.

If you think about the others for example gravity doesn’t make sense and neither does turgor so maybe it’s either friction or electricity
I hope I helped :)
7 0
2 years ago
4y-x<br> 3(2x+y)<br> when x = -3 and y = 3
yan [13]

Step-by-step explanation:

4×3-(-3)=12+3=15

3(2×(-3)+3)=3(-6+3)=(3×(-3)=-9

6 0
3 years ago
Suppose you throw a dart at a circular target of radius 10 inches. Assuming that you hit the target and that the coordinates of
sukhopar [10]

Answer:

a) The probability is 0.04

b) The probability is 0.36

c) The pprobability is 0,25

d) The probability is 0.09

Step-by-step explanation:

Lets calculate areas:

the target has a radius of 10 inces, hence the target area has a area on 10²*π = 100π square inches.

a) A circle of 2 inches of radius has an area of 2²π = 4π square inches, hence the probability of hitting that area is 4π/100π = 1/25 = 0.04

b) If the dart s within 2 inches of the rim, then it is not at distance 8 inches from the center (that is the complementary event). The probability for the dart to be at 8 inches of the center is 8²π/100π = 64/100 = 16/25 = 0.64, thus, the probability that the dart is at distance 2 or less from the rim is 1-0.64 = 0.36.

c) The first quadrant has an area exactly 4 times smaller than the area of the target (each quadrant has equal area), thus the probability for the dart to fall there is 1/4 = 0.25

d) If the dart is within 2 inches from the rim (which has probability 0.36 as we previously computed), then it will be equally likely for the dart to be in either of the 4 quadrants (the area that is within 2 inches from the rim forms a ring and it has equal area restricted on each quadrant). Therefore, the probability for the dice to be in the first qudrant and within 2 inches from the rim is 0.36*1/4 = 0.09.

6 0
3 years ago
What is the solution set of the following equation? 6x^2 = 13x + 5
fiasKO [112]

Answer:

2nd

Step-by-step explanation:

using the quadric formula

- ( - 13) +  -  \sqrt{( - 3) {}^{2} - 4 \times 6( - 5) }   \div 2 \times 6

do the math and you get the second one.

{-1/3,5/2}

6 0
3 years ago
Other questions:
  • (a) Use the Quotient Rule to differentiate the function f(x)=tan(x)-1/sec(x). f'(x)=
    13·1 answer
  • This table contains data on the number of people visiting a historical landmark over a period of one week. Using technology, fin
    5·1 answer
  • Solve the equation x^(2)-x=5x-25 over the complex numbers. Simplify the answer. Show your work.
    14·1 answer
  • The ratio of cats to dogs at the shelter is 3 to 2. if there are 16 cats at the shelter, how many dogs are there?
    14·1 answer
  • Yo can someone help me out
    15·1 answer
  • elena wants to paint her jewelry box blue.the jewelry box is in the shape of a cube and it has an edge length of 4 in. how much
    9·1 answer
  • 2) An $80 text book was on sale for $49.60 at the used book store. By what percent did the book decrease in price?​
    13·2 answers
  • Explain why you can find 5÷1/3 by multiplying 5 by 3.
    15·1 answer
  • Is 18,107,190 divisible by 3?<br><br><br>YES or NO<br><br><br>HELP ME PLZ I"M CRYING!
    14·2 answers
  • You want to buy a new car, but you don’t want to have a huge car loan payment every month, so you want to pay half of the $24,00
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!