Answers
Recall the half-angle identity for sine,
sin²(x/2) = (1 - cos(x))/2
Then the given equation is identical to
sin²(θ) = 1 - cos(θ)
Also recall the Pythagorean identity,
sin²(θ) + cos²(θ) = 1
Then we rewrite the equation as
1 - cos²(θ) = 1 - cos(θ)
Factoring the left side, we have
(1 - cos(θ)) (1 + cos(θ)) = 1 - cos(θ)
and so
(1 - cos(θ)) (1 + cos(θ)) - (1 - cos(θ)) = 0
and we factor this further as
(1 - cos(θ)) (1 + cos(θ) - 1) = 0
which gives
cos(θ) (1 - cos(θ)) = 0
Then either
cos(θ) = 0 or 1 - cos(θ) = 0
cos(θ) = 0 or cos(θ) = 1
[θ = arccos(0) + 2nπ or θ = -arccos(0) + 2nπ]
… or [θ = arccos(1) + 2nπ or θ = -arccos(1) + 2nπ]
(where n is any integer)
[θ = π/2 + 2nπ or θ = -π/2 + 2nπ] or [θ = 0 + 2nπ]
In the interval 0 ≤ θ < 2π, we get three solutions:
• first solution set with n = 0 ⇒ θ = π/2
• second solution set with n = 1 ⇒ θ = 3π/2
• third solution set with n = 0 ⇒ θ = 0
So, the first choice is correct.
Related Questions
The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses. Suppose in actuality that he can correctly identify finance majors 84% of the time, while 16% of the time he mistakenly identifies a music industry management major as a finance major. Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major), the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. Which of the following statements illustrates a Type I error?
a. Saying that the student is a finance major when in fact the student is a music industry management major.
b. Saying that the student is a music industry management major when in fact the student is a music industry management major.
c. Saying that the student is a finance major when in fact the student is a finance major.
d. Saying that the student is a music industry management major when in fact the student is a finance major.
Answers
Using error concepts, it is found that the option that represents a Type I error is:
d. Saying that the student is a music industry management major when in fact the student is a finance major.The definitions of each type of error are as follows:
A Type I error happens when a true null hypothesis is rejected. A Type II error happens when a false null hypothesis is not-rejected.
In this problem, the Hypothesis are:
Null: Student is a finance major.Alternative: Student is a music industry management major.By the definition of a Type I error, in this problem, it would consist in saying that a finance major student is a music industry management major student, hence option d is correct.
You can learn more about Type I and II errors at https://brainly.com/question/25225353
James is at the JL Long Run. He has exactly $32
and will purchase a shirt for $12. What percent of
his money will James spend on the shirt?
Answers
Part/whole= x/100
Let x= percentage of
money
12/32= x/100
1200/32= 37.5%
A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
D. 11
Answers
assuming the fraction is 1/11, the denominator shows how many parts the WHOLE was sliced into, namely 11 parts.
During a sale, a store offered a 15% discount on a camera that originally sold for $690. After the sale, the discounted price of the camera was marked up by 15%. What was the price of the camera after the markup? Round to the nearest cent.
Answers
Answer:674.475
Step-by-step explanation:
(690)(0.15)= 103.5
690-103.5= 586.5 (after first markdown)
(586.5)(0.15)= 87.975
586.5+87.975 (Final price after markup)
If 3(x − 2) = −7, then x =?
Answers
Answer:
-5 2/3
Step-by-step explanation:
is 3(x-2) = -7 then it's same as 3x-6=-7
We simplify this by adding 6 and subtracting 6.
Our result is
3x=-17
-17/3=-5 2/3
PLEASE HELP ME THIS IS THE 5TH TIME I HAVE HAD TO POST THIS AND GIVING BRAINLIST TO FIRST ANSWER
B.
C.
D.
Answers
Answer:
C.
Step-by-step explanation:
1 What is the universe made of? ...
2 How did life begin? ...
3 Are we alone in the universe? ...
4 What makes us human? ...
5 What is consciousness? ...
6 Why do we dream? ...
7 Why is there stuff? ...
8 Are there other universes?
Answers
1. big planets and carbon dioxide
2. when god sent adam (the first human being) to earth and had a female with him they got married and gave birth to children and the children marry each other and so on.
3. yes we're the only alive humans within this universe, but outside the universe are god and his worshippers.
4. our human-shaped bodies are the way we feel, hear, look, and do lots more things!
5. when someone feels unlike normal.
6. to feel there's a side of u that can do the impossible.
7. things were passed down from generations so it's possible that "stuff" can be made back when adam came to earth but other than that there was "stuff" even before humanity.
8. yes
other than that, hope u got ur questions solved
-3 (-3 - n) - 4 = 3n + 5
Answers
[tex]-3 (-3 - n) - 4 = 3n + 5\\\\\implies 9+3n -4 = 3n+5\\\\\implies 5 +3n = 3n+5\\\\\text{The equation is true for all values of n.}[/tex]
The factor that most heavily influences your credit score is
A. length of credit history
B. types of credit
C. amount owed
D. payment history
Answers
Answer:
D.payment history
Step-by-step explanation:
What does it mean to be an independent student? A. You must pick your own study topics and research them. B. You can set your own deadlines, within a fixed time frame. C. You are responsible for your own study schedule and organization. D. You are expected to work without extra help from a teacher or tutor.
Answers
Answer:
C
Step-by-step explanation
It makes the most sense
Answer:
check online for more information
Can someone pls answer them all?
Answers
a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.
Answers
==============================================================
Explanation:
For any prism, there are two congruent bases opposite one another. In other words, the bases are identical polygons with the same area. Each base is 5 square cm. So far, that accounts for 5+5 = 10 square cm of surface area. Let A = 10 as we'll use it later.
The perimeter is 12 cm and the height is 2 cm. It turns out that the lateral surface area is found by multiplying the two items. This is because the perimeter is made up of the lengths of the sides of the base, which when multiplied by the height, will give the area of each rectangular side panel.
So the lateral surface area is 12*2 = 24 sq cm. Let B = 24.
Overall, the total surface area is A+B = 10+24 = 34 square cm
Help
Geometry 1
Find z
Answers
Answer:
8
Step-by-step explanation:
The triangles are the same, except one is dilated.
So the hypotenuse of one is 5, and the other is 10. The triangle is dilated to double the other's size. so 4*2 = 8
I have no idea what i just wrote, but the answer is correct.
the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price
Answers
Answer:
Rs 8500
Step-by-step explanation:
For a cost price of c, the marked price is ...
marked = c +25%·c = 1.25c
After the 15% discount, the sale price will be ...
s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c
The profit will be the difference between the sale price s and the cost c:
p = s -c
500 = (1.0625c) -c = 0.0625c
Then the cost is ...
500/0.0625 = c = 8000
and the sale price is ...
s = c +p = 8000 +500 = 8500 . . . rupees
The selling price will be Rs 8500.
Find the value of x.
Answers
Answer:
9
Step-by-step explanation:
yeah, 9...........right???
1. Divide
(7x2 - 13x+4) - (x-1
)
Answers
Answer:7 x 2 − 14 x + 5
Step-by-step explanation:
1 In general, given a{x}^{2}+bx+cax
2
+bx+c, the factored form is:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 In this case, a=7a=7, b=-14b=−14 and c=5c=5.
7(x-\frac{14+\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})(x-\frac{14-\sqrt{{(-14)}^{2}-4\times 7\times 5}}{2\times 7})
7(x−
2×7
14+
(−14)
2
−4×7×5
)(x−
2×7
14−
(−14)
2
−4×7×5
)
3 Simplify.
7(x-\frac{14+2\sqrt{14}}{14})(x-\frac{14-2\sqrt{14}}{14})
7(x−
14
14+2
14
)(x−
14
14−2
14
)
4 Factor out the common term 22.
7(x-\frac{2(7+\sqrt{14})}{14})(x-\frac{14-2\sqrt{14}}{14})
7(x−
14
2(7+
14
)
)(x−
14
14−2
14
)
5 Simplify \frac{2(7+\sqrt{14})}{14}
14
2(7+
14
)
to \frac{7+\sqrt{14}}{7}
7
7+
14
.
7(x-\frac{7+\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})
7(x−
7
7+
14
)(x−
14
14−2
14
)
6 Simplify \frac{7+\sqrt{14}}{7}
7
7+
14
to 1+\frac{\sqrt{14}}{7}1+
7
14
.
7(x-(1+\frac{\sqrt{14}}{7}))(x-\frac{14-2\sqrt{14}}{14})
7(x−(1+
7
14
))(x−
14
14−2
14
)
7 Remove parentheses.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{14-2\sqrt{14}}{14})
7(x−1−
7
14
)(x−
14
14−2
14
)
8 Factor out the common term 22.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{2(7-\sqrt{14})}{14})
7(x−1−
7
14
)(x−
14
2(7−
14
)
)
9 Simplify \frac{2(7-\sqrt{14})}{14}
14
2(7−
14
)
to \frac{7-\sqrt{14}}{7}
7
7−
14
.
7(x-1-\frac{\sqrt{14}}{7})(x-\frac{7-\sqrt{14}}{7})
7(x−1−
7
14
)(x−
7
7−
14
)
10 Simplify \frac{7-\sqrt{14}}{7}
7 7− 14 to 1-\frac{\sqrt{14}}{7}1− 7 14
7(x-1-\frac{\sqrt{14}}{7})(x-(1-\frac{\sqrt{14}}{7}))
7(x−1− 7 /14 )(x−(1− 7 14 )) 11 Remove parentheses.
7(x-1-\frac{\sqrt{14}}{7})(x-1+\frac{\sqrt{14}}{7})
7(x−1− 7/ 14 .7(x−1+ 7 14 )
A computer can do 1000 operations in 4.5×10^-6 seconds. How many operations can be done by this computer in one hour?
Answers
Answer:
0.00027.
Step-by-step explanation:
All you have to do is do the scientific notation then multiply by 60.
The angle of depression from a window 10 m above the ground to a coin on the ground is 15°. Find the distance of the coin from the base of the building. Show your reasoning for each step.
Answers
if EF = 8x + 16, FG = 60, and eg = 156, find the value of x
Answers
Answer:
10
Step-by-step explanation:
8x+16+60=156
8x+76=156
8x=80
x=10
One kilometre is about 0.62 miles. It is 12 kilometres from Noah's house to the
ice skating rink. About how many miles is it from Noah's house to the ice
skating rink?
u'll get extra points if u answer guys!! pls help!!!!!
Answers
Answer:
7.44miles
Step-by-step explanation:
1km = 0.62miles
12km will be ; 0.62 × 12
= 7.44miles
how many 5 letter code words can be formed from the letters of the word MATRICES
Answers
113
Hope this helped you- have a good day bro cya)
please help me with math.
Answers
Answer:
Invalid
Step-by-step explanation:
This is invalid because you don't have to go some were to love something.
Answer:
Invalid
Step-by-step explanation:
All graduates love football;
This means all people who are graduates will love the football, it tells us nothing at all about people who are not graduates;
These people may love football or they may not;
Tom loves the football, thats all we are told;
He could, therefore, fall into either category, being a graduate since all graduates love the football or not being a graduate, since these might also love the football.
If I have a 1/4 chance of winning a bet, but lose it 40 times in a row, what percentage chance is that?
Answers
on tuesday a local a hamburger shop sold a combined total of 448 hamburgers and cheeseburgers , the number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold on tuesday ?
Answers
Hamburgers=1/4
448/4=112
112x3=336
Cheeseburgers=336
Hamburgers=112
112 hamburgers were sold on Tuesday.
13. Solve to find the vertex if :
3x2 – 19x - 5
Answers
Answer:
A) y = 3(x -3)^2 -46
B) (3, -46)
C) look at the y-coordinate of the vertex
Step-by-step explanation:
A) Factor the leading coefficient from the variable terms.
y = 3(x^2 -6x) -19
Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.
y = 3(x^2 -6x +9) -19 -3(9)
y = 3(x -3)^2 -46
__
B) Compared to the vertex form, ...
y = a(x -h)^2 +k
we find a=3, (h, k) = (3, -46).
The vertex is (3, -46).
__
C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.
If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.
Step-by-step explanation:
What is the greatest common factor shared by 40 and 20?
Answer here
SUBMIT
Answers
Answer:
20
Step-by-step explanation:
factors of 20 = 1 2 4 5 10 20
factors of 40 = 1 2 4 5 8 20 10
therefore 20 is the greatest common
A scientist crosses two pea plants that are
heterozygous for plant height and flower
color. Tall is dominant over short and purple is
dominant over white. The plant height and
Flower color genes are unlinked. Complete the
information below and the Punnett square.
Then answer the questions below.
Answers
The Punnett square is a diagram divided into squares that is used to determine genotypes.
The question is incomplete, as the required details such as the characters that represent the plant heights and the flower colors are not given.
So, I will give a general explanation instead.
Assume the plants that are crossed are represented as: TT and Tt.
The possible genotypes would be TT, TT,Tt and Tt
In the above list of genotypes, genotype T is dominant over genotype t
See attachment for an illustration of the Punnett square.
Read more about Punnett square at:
https://brainly.com/question/15723456
Helppppp pleaseee????
Answers
Answer:
Lower quartile 3, median 5, Upper quartile 7
Step-by-step explanation:
First divide the data in half 1 3 4 and 6 7 7
The median is the middle between 4 and 6, so it is 5.
The lower quartile is the median in the lower half, 3
The upper quartile is the median in the upper half, 7
Billy invests $5,000 in an account at 4.2% for 15 years, compounded monthly. Assuming no other deposits or withdrawals are made, how much will Billy have at the end of 15 years?
Answers
The amount Billy has at the end of the 15 years is $9,377.73.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P[tex](1 + r/n)^{nt}[/tex]
P = principal
r = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $5000
r = 4.2%
t = 15 years
n = 12
A = P[tex](1 + r/n)^{nt}[/tex]
A = 5000 [tex](1 + 0.0035)^{180}[/tex]
A = 5000 x [tex]1.0035^{180}[/tex]
A = $9,377.73
Thus,
Billy has $9,377.73 at the end of the 15 years.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ2
solve the log equation
Answers
Answer:
x = -5
Step-by-step explanation:
log5((5-3x)/((7+x)^2))=1
(5-3x)/(7+x)^2 = 5
5-3x = 5x^2+70x+245
5x^2+73x+240=0
x= -5, x= -48/5
-48/5 is extraneous
x = -5