Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.
Answers
The equations which completes the left-hand column of the table are;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Which equations and identities complete the left-hand column of the table?The given expression on the right is written as follows;
First row;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
The definition of the sum and difference of cosine are;
cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)
cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)
Therefore;
Second row;
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)
Which gives;
[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
Third row;
sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Learn more about trigonometric functions here:
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Related Questions
98 x 24 = (100 - 2 ) x 24 = ?
Answers
Answer:
2352
Step-by-step explanation:
(100 - 2) x 24 = 2400 - 48 = 2352
Find the radius and the diameter to the nearest hundredth when C = 7π yd. Use 3.14 for π.
60 POINTS PLEASE GIVE VALID ANSWER
Answers
Answer:
Diameter = 7
Radius = 3.5
Step-by-step explanation:
Hi! Ace here.
So, the formula to find circumference is dπ or 2rπ
So to find the diameter, you do the circumference/π
To find the radius, you'd do the circumference/2π
Plug-in those numbers and there you go!
Hope this helps, let me know if you have any questions.
I know this was a very vague explanation so I encourage you to ask any questions. Thank you!
Give that the line m is parrallel to the line r and m<IHB = (5y+39)° and m<HBC =(3y+85)° ,find m<CBG SHOW ALL WORK
Answers
Answer:
5y+39=3y+85 that is 5y-3y=85-39= 2y=46 and the answer is y=23
Hi. i need these exercises pls
(+2)+(+7)=..
(-3)+(-4)=..
(+7)+(-3)=..
(-2)+(+9)=..
(-3)+(+3)=..
Answers
2=-7
3=4
4=7
5=0
Mark as Branilist
least common denominator of 2/9 and 11/12 ?
Answers
Answer:
2/9
Step-by-step explanation:
find the volume and the total surface area of a cube whose edge is 1.5m.
Answers
Answer:
I think it's 18
Step-by-step explanation:
1.5 x 1.5 is the first area of a single side, which is 3. 3 x 6 is 18.
sorry if this is wrong!
plz help
............
Answers
Hi there!
[tex]\large\boxed{x < 2}[/tex]
[tex]\frac{4x + 6}{7} < 2[/tex]
Begin by multiplying both sides by 7:
[tex]4x + 6 < 2 * 7 \\\\4x + 6 < 14[/tex]
Subtract 6 from both sides to isolate for x:
[tex]4x + 6 - 6 < 14 - 6\\\\4x < 8[/tex]
Divide both sides by 4 to solve for x:
[tex]4x/4 < 8/4\\\\x < 2[/tex]
I need help pls how do u do this step by step? ):
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However with b, if your stock drops by 25% then goes up by 35% overall you only have a +5%.
Answer: A.
Hope this helps :)
-4x = 8
what is it??
Answers
Answer: if your solving for x it’s -2
Step-by-step explanation:
Answer:
x is -2
Step-by-step explanation:
because -4 x -2 is 8
me pueden ayudar plis lo necesito para hoy
Answers
Answer:
4)B
Step-by-step explanation:
0
0.25
0.50
0.75
Select all the expressions equivalent to 2.8⁴.
A. 6.8
B. 2.8 + 2.8 + 2.8 + 2.8
C. 11.2
D 2.8 + 4
E. 2.8 × 2.8 × 2.8 × 2.8
F. 61.4656
G. 2.8 × 4
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Select all the expressions equivalent to }\mathsf{2.8^4}[/tex]
[tex]\large\text{Exponents is a number that is being said how many times to use}\\\large\text{when you are multiplying}[/tex]
[tex]\large\text{Now lets try to solve for your answer(s)}[/tex]
[tex]\bold{2.8^4 = 2.8\times2.8\times2.8\times2.8}\\\bold{2.8\times2.8\times2.8\times2.8}\\\bold{2.8\times 2.8 = 7.84}\\\bold{7.84\times7.84= answer}\\\uparrow\large\text{Solve above and you should have one of your answers!}\\\bold{\rightarrow 7.84\times7.84= 61.4656}[/tex]
[tex]\bold{2.8^4\ is\ EXPRESSED\ approximately\ 4\ times}\\\\\bold{\rightarrow 2.8^4= 2.8\times2.8\times 2.8\times2.8}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \underline{\bf{Option E.) 2.8 * 2.8 * 2.8 * 2.8 \& Option F. 61.4646}}}}}\huge\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Jason wanted to place all 540 marbles in the 3 newly bought boxes. If he wants to
divide it in a ratio of 1:2:3, how many marbles would be in each box?
I really need your help please!!, thank you.
Answers
Answer:
The first box will have 90 marbles, the second 180 and the third 270.
Step-by-step explanation:
Division in a ratio of 1:2:3
1 + 2 + 3 = 6
So
The first box will have 1/6 of the marbles.
The second box will have 2/6 = 1/3 of the marbles
The third box will have 3/6 = 1/2 of the marbles.
First box:
One sixth, so:
(1/6)*540 = 540/6 = 90
Second box:
One third, so:
(1/3)*540 = 540/3 = 180
Third box:
One half, so:
(1/2)*540 = 540/2 = 270
The first box will have 90 marbles, the second 180 and the third 270.
Solve the quadratic equation numerically (using tables of x- and y- values).
(x +2) (x + 3) = 12
a.
x = -1 or x = 3
c.
x = -6 or x = 1
b.
x = 2 or x = -3
d.
x =1 or x = -1
Please select the best answer from the choices provided
A
B
C
D
Answers
benceA yada D bilemedim
Answer:
to whoever else needs it, the answer is c
Step-by-step explanation:
just trust me bro
X squared + 3x - 4 = 6
Answers
Hi there!
3x-4=6
To find x, add 6 with 4 then divide by 3...
[tex]6+4=10[/tex]
[tex]10[/tex]÷[tex]3=\frac{1}{3}[/tex]
Final Result: x=1/3
Whyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy me
I do not like school What is
9 times 9 times 9
Answers
Answer:
729
Step-by-step explanation:
9x9x9
Answer:
9*9*9 = 729
Step-by-step explanation:
This can also be expressed by 9^3 (Nine cubed)
9 times 9 is equal to 81. 81 times 9 is equal to 729
There you go!
PS: Give school a chance, I know it's hard during this special time, but once this fades away, you might enjoy it a bit more. :D
Plz help I’m stuck on this question
Answers
Answer:
the answer is C
Step-by-step explanation:
bhl
2
i hope it will help you
The population of a city decreases by 1.2% per year. If this year's population is
242,000, what will next year's population be, to the nearest individual?
Answers
Answer:
Your answer
212960
Mark it as Brainlist answer. Follow me to get more answer
Step-by-step explanation:
Answer: it is actually 239096
Step-by-step explanation:
Parallelogram ABCD is similar to parallelogram EFGH. Which proportion must be true?
A. BC FG = CD GH
B. FG BC = CD GH
C. AB HG = CB FG
D. BA EH = CD FG
Answers
Answer:
I believe the answer is D
Step-by-step explanation:
that one made them ost sense to me but I'm sorry if I'm wrong
3. A process that occurs resulting in a organism becoming more complex structurally.
Answers
Answer:
Development
Step-by-step explanation:
HELP PLEEEASE DUE TODAY ALL MY POINTS
if ΔABC and ΔXYZ are similar which must be true
Answers
You must match the letters.
Answer:
C)
Step-by-step explanation:
Hope that helps!
ANSWER ASAP I WILL GIVE BRAINLIST
Answers
1) In statistics, the average is also
known as
O a) Mean
b) Median
c) Tally Marks
O d) Mode
Answers
Answer:
In statistics the average is also known as mean.
The average is also known as mean.
Please please give answer for this question
Answers
Answer:
each side of the hexagon measures 40 cm (which agrees with answer B)
Step-by-step explanation:
Recall that a regular hexagon has six equal sides, therefore, each side would be one sixth of the 240 cm:
each side of the hexagon = 240 cm / 6 = 40 cm
find the interest rate you are borrowing $2,500 for 2 years and you ear $450 in interest
Answers
Answer:
2500×100/2×450
25/2×450
25/900=
36
Create a word problem that can be represented by the expression in number 4. –6 ÷ 1 1/3
Answers
Answer:
I suppose that we want to use the expression in number 4.
The expression we need to use is:
6/(1 + 1/3)
This is:
"the quotient between the number 6 and the number 1 and 1/3"
We could write a problem like:
"We have 1 and 1/3 pounds of apples, and we have 6 grams of caramel that we want to divide evenly between all the apples. How much caramel we will have in each pound of apples?"
Then we need to divide the total amount of caramel by the total amount of apples, this is:
(6gr)/(1 + 1/3 lb) = (6/(3/3 + 1/3 )) gr/lb = (6/ 4/3) gr/lb = 6*(3/4) gr/lb
= 18/4 gr/lb = (16 + 2)/4 gt/lb = 16/4 gr/lb + 2/4gr/lb = 4 gr/lb + 1/2 gr/lb
= (4 and 1/2) gr/lb
If a=-9 and b= -4, what is the value of a + b?
0-5
5
-13
13
Answers
Answer:
The answer is -13.
Step-by-step explanation:
-9 + -4 = -13
math help ohh yup #5 in the middle
Answers
Answer:
m<7 = 49°
m<8 = 41°
m<9 = 49°
m<10 = 41°
Step-by-step explanation:
Given :
m<7 ≅ m<9
m<8 = 41°
m<7 = 90° - m<8 (complementary angles)
m<7 = 90° - 41° (substitution)
m<7 = 49°
m<9 = m<7 (m<7 ≅ m<9)
m<9 = 49° (substitution)
m<10 = 90 - m<9
m<10 = 90 - 49
m<10 = 41°
Susie is 13
5
6
years old. Dwight is 1
1
3
years older than Susie and Jane is 1
1
4
years older than Dwight. How old is Jane?
Answers
Answer: what
the way you worded the question makes no sense
Find the slope of the line passing through each of the following pairs of points. (0,0) (4,3)
Answers
Answer:
Step-by-step explanation:
Slope or m is defined as
m=(y2-y1)/(x2-x1) in this case
m=(3-0)/(4-0)
m=3/4
Find the area.
3 ft.
9 ft.
4ft.
5 ft.
Cid +