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
notka56 [123]
2 years ago
10

Use a double angle or half angle identity to find the exact value of each expression

Mathematics
1 answer:
STatiana [176]2 years ago
4 0

Answer:

Step-by-step explanation:

There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.

We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:

3^2=1^2+y^2 which simplifies to

9=1+y^2 and

y^2=8 so

y=\sqrt{8}=2\sqrt{2} so that's the missing side. Now we can easily determine that

sin\theta=\frac{2\sqrt{2} }{3}

Now we have everything we need to fill in the identity for sin2θ:

2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3}) and multiply all of that together to get

2sin\theta cos\theta=\frac{4\sqrt{2} }{9}

You might be interested in
A father and a son were driving they had a car crash accident and the father died, the ambulance took the boy to the hospital bu
Arada [10]

Who says the mother can’t be the surgeon?

8 0
3 years ago
Read 2 more answers
Two bags with 3 oranges in each bag is the same amount as 3 bags with 2 oranges in each bag. Which property of multiplication do
kodGreya [7K]

Answer:

Commutative Property

Step-by-step explanation:

The property of multiplication that is being demonstrated is known as Commutative Property. This property basically shows that when multiplying two numbers the actual order in which they are multiplied does not matter and does not affect the result at all. For example, the in this scenario to get the total number of oranges we have to multiply the number of bags by the number of oranges in each bag, but whatever way we do this they equal the same

2 bags * 3 oranges per bag = 6 oranges

3 bags * 2 oranges per bag = 6 oranges

Therefore,

2 * 3 = 3 * 2

7 0
2 years ago
Solve. 3(x-6)-2(2x+3)=14
coldgirl [10]

Answer:

x=-38

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(x−6)−2(2x+3)=14

(3)(x)+(3)(−6)+(−2)(2x)+(−2)(3)=14(Distribute)

3x+−18+−4x+−6=14

(3x+−4x)+(−18+−6)=14(Combine Like Terms)

−x+−24=14

−x−24=14

Step 2: Add 24 to both sides.

−x−24+24=14+24

−x=38

Step 3: Divide both sides by -1.

−x

−1

=

38

−1

x=−38

5 0
3 years ago
Read 2 more answers
There are 30 families. Two families have 4-5 pets. What percent of the families own 4-5 pets?
amm1812
2/30=0.06 repeated. 0.06=6%. 7% or 6.6% of the 30 families have 4-5 pets.
3 0
3 years ago
Can the exponent in the denominator be subtracted from the exponent in the numerator when the based are different? Explain
Vanyuwa [196]

Answer:

No, Sorry.

Step-by-step explanation:

Since the bases are different, you'll have to change them even if they have a exponent or not. If you dunno how to make the denominators the same, just multiply the two by eachother.

Example) 1/2 - 3/4

\frac{1}{2}  -  \frac{3}{4}

Multiply 2 and 4 together, and then multiply the 4 to the one also. Multiply 2 to four and also to the 3.

\frac{4}{8}  -  \frac{6}{8}

The subtract from there.

\frac{ - 2}{8}

and then Reduce (if needed.)

\frac{ - 1}{4}

4 0
3 years ago
Other questions:
  • A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales tota
    14·1 answer
  • Find the missing side length.
    5·1 answer
  • Help, how do u find h?
    5·1 answer
  • PLEASE HELP!! SHOW WORK!!A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of pickin
    10·1 answer
  • (a)
    7·1 answer
  • Please help this is the last question!!!!
    15·2 answers
  • Daniel combines 6.42 liters of red paint with 6.87 liters of blue paint to make purple paint. He pours the paint equally into 3
    5·1 answer
  • Pleas help!<br><br> WILL THANKS YOUR ACCONT and MARK BRAINLIEST
    12·1 answer
  • If mZDEF= 117°, find the value of x.
    6·1 answer
  • Help me please I beg of you
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!