I need to solve for the angle, but I just don't know how to do it! The equation is: Cos A=Sin3A
Can someone explain the formula so I can know how to do it, I will really appreciate it!
Answers
9514 1404 393
Answer:
A = 22.5°, 45°, 112.5°, 202.5°, 225°, 292.5°
Step-by-step explanation:
Use the angle reduction formula to reduce this to an expression involving only sine or cosine, then solve the resulting higher-degree polynomial.
sin(3x) = 3sin(x) -4sin³(x)
Using the identity for cosine, we have the radical equation ...
√(1 -sin²(A)) = 3sin(A) -4sin³(A)
Squaring both sides, we have ...
1 - sin²(A) = 9sin²(A) -24 sin⁴(A) +16sin⁶(A)
Letting z = sin²(A), this is the cubic equation ...
1 -z = 9z -24z² +16z³
16z³ -24z² +10z -1 = 0
Solving this by the usual methods, we find its factors to be ...
(2z -1)(8z² -8z +1) = 0
8(2z -1)((z -1/2)² -1/8) = 0 . . . . quadratic in vertex form
Then the roots are ...
z = (1 ±√(1/2))/2, z = 1/2
The angle solutions are ...
A = arcsin(±√z)
Of course, these need to be adjusted to fall in the domain of interest, and checked for extraneous solutions.
For z = 1/2-√(1/8), the angles are ...
A = ±22.5° ⇒ 22.5°, 157.5°, 202.5°, 337.5°
For z = 1/2, the angles are ...
A = ±45° ⇒ 45°, 135°, 225°, 315°
For z = 1/2+√(1/8), the angles are ...
A = ±67.5° ⇒ 67.5°, 112.5°, 247.5°, 292.5°
The angles that are in bold are the actual solutions; the others are extraneous.
_____
All of the above is "the hard way." A much simpler approach is to take advantage of the identity ...
cos(a) -sin(b) = (1/2)·sin(b/2 -a/2 -π/4)·sin(b/2 +a/2 -π/4)
Then you can use the zero product rule to find (for a=A, b=3A) ...
(3A/2 -A/2 -π/4) = nπ ⇒ A = nπ +π/4 ⇒ 45°, 225°
(3A/2 +A/2 -π/4) = nπ ⇒ A = (nπ +π/4) ⇒ 22.5°, 112.5°, 202.5°, 292.5°
_____
Rewriting the equation as a function equal to zero, the solutions are the x-intercepts of the graph. In the attached, the x-axis is set to degrees.
f(A) = cos(A) -sin(3A) = 0
Related Questions
Question 5
1 pts
5) If a person runs 1/3 mile in 1/9 of an hour, what is
the unit rate per hour?
A. 1/9 mi/hr
B. 1/3 mi/hr
C. 3 mi/hr
D. 9 mi/hr
Answers
which number is a possible solution to the inequality below?
x£ -3
A -4.75
B -2.25
C 1.25
D 3.75 £ <------ this btw is a less sign but a line under it (please help thanks)!!
Answers
Answer:
A -4.75
Step-by-step explanation:
The inequality is given as :
x ≤ -3
A possible solution per the answer choices is -4.75
Hence;
-4.75 ≤ -3
Explain whether each is a linear equation
y = 1 - x
Answers
Answer:
In a linear equation in x and y, x is called x is the independent variable and y depends on it. We call y the dependent variable. If the variables have other names, yet do have a dependent relationship, the independent variable is plotted along the horizontal axis
:)
Answer:
This should be considered a linear substitution because you can substitute this equation into y in another linear equation to find the answer or the solution to the linear equation
Step-by-step explanation:
The formula for the perimeter (P) of a rectangle is
P= 21 + 2w, where / represents the length and w represents
the width. What is the perimeter ofa rectangle that has a length of 68 centimeters and a width of 19 centimeters?
Answers
Answer:
174
Step-by-step explanation:
L = 68
W=19
Use the formula given:
2 x 68 + 2 x 19 = 174
Simplify √(112x^2y). Please help!!
Answers
Answer:
4x.sqrt(7y)
Step-by-step explanation:
Answer:
4x^y(square root) 7
Step-by-step explanation:
How do I solve this problem? Please show me!
Answers
9514 1404 393
Answer:
arc AB = 12.4 cm
Step-by-step explanation:
The length of arc AB is 1/4 of the circumference of the circle, so is ...
AB = (1/4)(2πr)
= (π/2)r = (3.14/2)(7.9 cm) = 12.403 cm
Rounded to the nearest tenth, arc AB = 12.4 cm.
Sarah bought a car for $3500 and later sold it for
a 30% profit. How much profit did Sarah make in
the car?
Answers
Answer: 10
Step-by-step explanation:
budda dawg
1. Write a system of equations to describe the situation. Then solve the system. Be sure to define your variables! Rizzo has $1.50 less in his piggy bank than his sister Shonda. If Shonda had $9 more, she would have three times as much money as Rizzo. How much money do each of the children have in their banks?
Answers
Answer:
The amount Rizzo has = x = $5.25
The amount Shonda has = y = $6.75
Step-by-step explanation:
Let us represent:
The amount Rizzo has = x
The amount Shonda has = y
Rizzo has $1.50 less in his piggy bank than his sister Shonda.
x = y - 1.50.......Equation 1
If Shonda had $9 more, she would have three times as much money as Rizzo.
y + 9 = 3(x)
y + 9 = 3x..... Equation 2
y = 3x - 9
We substitute 3x - 9 for y in Equation 1
x = y - 1.50.......Equation 1
x = 3x - 9 - 1.50
9 + 1.50 = 3x - x
10.50 = 2x
x = 10.50/2
x = $5.25
Solving for y
y = 3x - 9
y = 3(5.25) - 9
y = $6.75
Therefore:
The amount Rizzo has = x = $5.25
The amount Shonda has = y = $6.75
2 dot plots. The highlands have a mean rainfall of 15.27 millimeters, and the Lowlands have a mean rainfall of 12.05 millimeters.
Analyze the dot plots. What is the approximate difference between the means of the two data sets to the nearest whole number?
Answers
Answer:
it's 3mm
I hope this helped
Answer:
the answer is 3mm
Step-by-step explanation:
i did the answer and got it correct
Three vertices of quadrilateral ABCD are A(-4,3), B(-1,5), and D(4,-1), as shown below.
In order for ABCD to be a parallelogram, what must be the coordinates of point C?
A. (-1, -7)
B. (1.5, 2)
C. (2, -4)
D. (7, 1)
Answers
Answer:
my answer is letter c thats may answer
HELPPPPPPPPPPPPPPPPPPPPPPP
The temperature at 7:00 a.m. was –9°F. By 4:00 p.m., the temperature had risen 10 degrees. What was the temperature at 4:00 p.m.?
Group of answer choices
-19
19
-1
1
Answers
Answer:
1
Step-by-step explanation:
-9+10=1
Answer:
1
Step-by-step explanation:
helpppppppppppppppppppppppppppp
Answers
Answer: i know p4 but what does the first q say?
Step-by-step explanation:
Answer:
2nd one
Step-by-step explanation:
Can someone help me please, ill give brainy
Answers
Answer:
x = -6
Step-by-step explanation:
The value of x never changes, no matter what the value of y is, so x = -6 describes every point on the line.
Explain please I’m stuck
Answers
FYI - the length of the mid-segment of a trapezoid is equal to half the sum of the lengths of its bases.
the equation:
18 + 6x - 12 = 2(2x + 10)
18 + 6x - 12 = 4x + 20
6 + 6x = 4x + 20
6x = 4x + 14
2x = 14
x = 7
3 1
(3.0 x 10 ) (5.0 x 10 ) = ?
Answers
Answer:
1500
Step-by-step explanation:
Parenthesis first, 3x10 is 30 5x10 is 50, 50x30 is 1500
A map has the scale 2 inches equals 190 miles. The distance from Springfield to Glenview is 14 inches. How many actual miles separate Springfield from Glenview?
A.
140
B.
2,800
C.
1,330
D.
38
Answers
Answer:
It would be C because
Step-by-step explanation:
2= 190
So what i did was i divide 190 to 2 and i got 95
and to the 14 I multiply it o 95 and i got 1,330
How i got 1,330 is that i read the question and looked at the answers which is a bigger number. So i thought it ain't adding or subtracting. So i decided to do dividing 190/2= 95 then i multiplied 14 to 95
The product of two positive consecutive integers is 12. Find the
integers. *
Answers
Answer:
3, 4
Step-by-step explanation:
The choices for the consecutive integers are: 6, 7, 4, 5 or 3, 4
Test the products of these integers.
6 x 7 = 42
4 x 5 = 20
3 x 4 = 12
The only pair of consecutive integers with 12 as their products is 3 and 4.
Find the next two numbers in the number pattern.
6, 12, 9, 18, 15,
Answers
Answer:
30
Step-by-step explanation:
Starting number is 6, doubled, then returned to original number and added 3, then 6, then so on. Next set of numbers would be:
30, 24, 48, 38...
Samantha says the fraction of the group of customers who ordered raspberry topping is 1/2. Explain why samantha is correct.
Answers
Answer and explanation:
Yes Samantha is correct. Samantha is correct because a fraction 1/2 of customers who ordered raspberry toppings refers to half of the total number of customers. A fraction 1/2 is 50 percent or 50/100 of the population of customers, therefore meaning that 50% or half of the total number of group of customers ordered raspberry toppings
PEDRO QUIERE SABER CUÁNTO PAPEL DE REGALO TENDRÍA QUE USAR PARA PODER FORRAR UNA CAJA CUADRADA DE 30 cm POR LADO.
Answers
PLEASE HELP!! WILL GIVE BRAINLEST ANSWERS
Answers
Answer:
4th one
Step-by-step explanation:
it is the 4th one
Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym after x months and spends the rest of the year, y months, with the second gym. The membership to the first gym costs $85 per month, while the membership for the second gym costs $50 per month. If she ended up spending a total of $705 over the course of the year, how much time did she spend at each gym?
Answers
Answer:
Jan spent 3 months at the first gym and 9 months at the second gym.
Step-by-step explanation:
Given that:
1 year = 12 months
x = months at gym one
y = months at other gym
According to given statement;
x+y=12 Eqn 1
85x+50y=705 Eqn 2
Multiplying Eqn 1 by 50
50(x+y=12)
50x+50y=600 Eqn 3
Subtracting Eqn 3 from Eqn 2
(85x+50y)-(50x+50y)=705-600
85x+50y-50x-50y=105
35x=105
Dividing both sides by 35
[tex]\frac{35x}{35}=\frac{105}{35}\\x=3[/tex]
Putting x=3 in Eqn 1
3+y=12
y=12-3
y=9
Hence,
Jan spent 3 months at the first gym and 9 months at the second gym.
Kane is training for a Marathon. He starts by eunning 2 miles during every yriang sessiom. Each week plans to increase the distance of his run 1/4 mile
Answers
Question:
Write and expression to show the distance Kane runs in a training session after w weeks
Answer:
[tex]d = 2 + \frac{1}{4}w[/tex]
Step-by-step explanation:
Given
[tex]Initial = 2\ miles[/tex]
[tex]Rate= \frac{1}{4}[/tex]
Required
Write an expression
Let the distance covered in w weeks be d.
The expression for d is derived by:
[tex]d = Initial + Rate * w[/tex]
Substitute values for Initial and Rate
[tex]d = 2 + \frac{1}{4}* w[/tex]
[tex]d = 2 + \frac{1}{4}w[/tex]
Solve For X
please help, thank you :}
Answers
Answer:
4
Step-by-step explanation:
X = 4
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PLEASE ANSWER I WILL GIVE YOU BRAINIEST IF CORRECT!!!!!!!
thanks!
Answers
Answer:
700 is your answer
Step-by-step explanation:
ok so 5x120=600 +100=700 so 700 is your answer
Solve for x.
3(x - 4) = 2x + 6
ΟΑ. Ο
B. 2
C. 3.6
D. 10
E. 18
Answers
Answer:
the answer is D. 10
Step-by-step explanation:
you get 3x -4 = 2x +6
you then subtract 2x from 3x and 2x
you get 1x - 4= 6
add 4 to both sides and you get
1x = 10 which is the same as x = 10
Answer:
x = 18
Step-by-step explanation:
3(x-4) = 2x+6
3x-12 = 2x +6
Add 12 to the -12 and the 6, giving you...
3x = 2x + 18
subtract 2 from the 3 and the 2, giving you...
1x = 18
divide the 1 and the 18 by 1, giving you...
x = 18
I hope this helps you out!
A physical therapy student is adding up the cost of books for the first three semesters of school. The first semester he spent $400, the second semester he spent $515, and the third semester he spent $620. What on average has he spent on books per year?
Answers
Answer:
Im not sure but i think 1535
Step-by-step explanation:
Alex paid $6 for renting a movie for 3 days. Which graph shows the relationship between the cost of renting the movie for different days
Answers
Answer:The graph will show that on 0 days it costs 0 dollars. On day 1,2, and 3 it will be $6
Step-by-step explanation:I hope this helps! Have a great day
Can someone please help me with this question?
Answers
Answer:
Pretty sure added to
Step-by-step explanation:
The reason why it is added to because the plus sign adds stuff and it doesn't subtract, multiply, or divide.
Hope this helped!! :)
Brainliest?!?!
help pls i have 3 tests to do and this is due today
Answers
Answer:
The sum of any triangle is 180 degrees.
Step-by-step explanation:
Answer:
a = 60
b = 60
c = 60
d = 42
e=35
f=35
g=55
h=45
i=45
j=15
k=15
l=75
m=120
n=21
o=69
p=21
q=55
r=55
s=42
t=42
u=69
Step-by-step explanation:
