Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side of b lies in quadrant 2
Answers
Answer:
cos(a + b) = [tex]\frac{1}{12}(1-2\sqrt{30})[/tex]
Step-by-step explanation:
cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]
cos(a) = [tex]-\frac{1}{3}[/tex]
cos(b) = [tex]-\frac{1}{4}[/tex]
Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.
sin(a) = [tex]-\sqrt{1-(-\frac{1}{3})^2}[/tex] [Since, sin(a) = [tex]\sqrt{(1-\text{cos}^2a)}[/tex]]
= [tex]-\sqrt{\frac{8}{9}}[/tex]
= [tex]-\frac{2\sqrt{2}}{3}[/tex]
Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.
sin(b) = [tex]-\sqrt{1-(-\frac{1}{4})^2}[/tex]
= [tex]-\sqrt{\frac{15}{16}}[/tex]
= [tex]-\frac{\sqrt{15}}{4}[/tex]
By substituting these values in the identity,
cos(a + b) = [tex](-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})[/tex]
= [tex]\frac{1}{12}-\frac{\sqrt{120}}{12}[/tex]
= [tex]\frac{1}{12}(1-\sqrt{120})[/tex]
= [tex]\frac{1}{12}(1-2\sqrt{30})[/tex]
Therefore, cos(a + b) = [tex]\frac{1}{12}(1-2\sqrt{30})[/tex]
Related Questions
In a collection of coins, the number of quarters is one-third the number of pennies. The number of quarters is Q. The number of pennies is P. What is the correct formula relating Q to P
Answers
Answer:
Q = P/3
Step-by-step explanation:
Let the number of quarters be Q
Let the number of pennies be P
If the number of quarters is one-third the number of pennies, this can be expressed as;
Number of quarter = 1/3 of pennies
Q = 1/3 of P
Of means multiplication
The expression becomes;
Q = 1/3 × P
Q = P/3
Hence the formula relating Q to P is
Q = P/3
What are all the ways to multiply
Answers
Answer:
multiplying :v
Step-by-step explanation:
................
What is the y-intercept?
(20,0)
0 (0, 18)
(18,0)
O (0,20)
Answers
Liam has a bag of b beads. He gives 20 beads to his sister. He then makes 4 necklaces with the same number of beads on each necklace using all of the remaining beads. Write an expression that represents the number of beads on each necklace. Show your work.
Answers
Answer:
5
Step-by-step explanation:
just do 20 divided by 4 and you will get 5. Also, do 5x4 to make sure you let your teacher know that you got the right answer.The expression in one variable b that shows the number of beads on each necklace is (b-20)/4
What is an expression in one variable?An expression in one variable is a statement formed by the using constants and an unknown variables and mathematical operators but sign is equal to is not used. Expression in one variable is linear if the power of the unknown variable is equal to one .
Standard form of linear expression in one variable x is ax +b , where a and b are constants .
Given that Liam has a bag of b beads
He gave 20 beads to his sister
Then, remaining beads = b -20
Remaining beads are used to make 4 necklaces
Let the beads on each necklace be x
Then beads in four necklaces = 4x
As, Remaining beads = beads in four necklaces
⇒4 x = b - 20
Dividing the equation by 4 on both sides
⇒ x = (b-20)/4
∴ The expression that shows the number of beads on each necklace is (b-20)/4
Also, Learn more about the expressions in one variable from the link below:
brainly.com/question/17272650
#SPJ1
Which line has a slope of
a
and a y-intercept of 2?
Answers
Answer:
it is 3
Step-by-step explanation:
G
Which number line can be used to find the distance between (-1, 2) and (-5, 2)?
--7-6-5
-3-2
0
1
2
3
-2 -1 0
1
2
3
5
6 7
8
-7 -6 -5 4 3 - -
0 1
2
3
1
2
3 4 5
Answers
9514 1404 393
Answer:
see below
Step-by-step explanation:
The y-coordinates of the points are the same, so the distance between those points will be the difference of the x-coordinates. The first number line shows those x-coordinates plotted properly. It can be used to find the difference between them.
Prove the identity.
TT
sin x +
2.
cotx
sin (-x)
Answers
Answer:
Hi... Do this for prove that
Answer:
Step-by-step explanation:
Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 81
Answers
Based on the diagram, the expression which shows the possible length of segment AB shows that 27 < AB < 81
A triangle that does not have equal sides and angles is known as a scalene triangle.
From the figure attached below, let's have a triangle ABC by using the parameter in the instructions given.
where;
side |AC| = 27side |CB| = 54side |AB| = ???We can use the Pythagoras rule to determine the side |AB|.
Pythagoras rule states that the sum of the hypotenuse squared is equal to both the sum of the opposite squared and adjacent squared.
hyp² = opp² + adj²
AC² = AB² + CB²
54² = AB² + 27²
[tex]\mathbf{AB^2 = 54^2 - 27^2}[/tex]
[tex]\mathbf{AB^2 = 2187}[/tex]
[tex]\mathbf{AB =\sqrt{ 2187}}[/tex]
AB = 47
Therefore, we can conclude that the expression which shows the possible length of segment AB shows that 27 < AB < 81.
Learn more about triangles here:
https://brainly.com/question/12852445
Answer: 27<AB<81
Step-by-step explanation:
just took test
72 times what gives you 6834
Answers
Answer:
94.917
Step-by-step explanation:
6834/72 = 94.916666
if six pounds of grape juice is $3, how much would it cost to buy 3,4, and 5 pounds of grape juice?
Answers
Answer:
It would cost $9 for 3 pounds, $12 for 4, and $15 for 5.
Step-by-step explanation:
I hope I understood what you we're asking correctly, sorry if not. :)
If the sales tax for the city of Los Angeles is 9.75%.how much tax would you pay for an item that costs $200.00
Answers
Sky bought $22.50 worth of paint supplies at a store that sells brushes for $1.50 each and tubes of paint for $2.50 each. Let b
represent the number of brushes bought and t
represent the number of tubes bought.
Which one of the following could not be true about the values of b
and t
?
b=0
and t=9
b=6
and t=5
b=10
and t=3
b=15
and t=0
Answers
Answer:
b = 10 , t = 3
Step-by-step explanation:
which shape is similar to shape l?
Answers
Answer:
pentagon
Step-by-step explanation:
got 5 sides
what is x equal to ?????????
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Answer:
x is 6
Step-by-step explanation:
Answer: Hope this helps you love!
Step-by-step explanation:
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please help 6th grade math i will mark brainliest to 1 answer select all that are equivalent to 15%
Answers
Answer:
.15
Step-by-step explanation:
Answer:
.15, 3/20
Step-by-step explanation:
An arts academy requires there to be 5 teachers for every 95 students and 4 tutors for every 40 students how many students does the academy have per teacher? Per tutor
Answers
Answer:
19 students per teacher and 10 students per tutor
Step-by-step explanation:
To find the amount of students per teacher and per tutor you have to divide
95 students /5 teachers
19 students per teacher
40 students /4 tutors
10 studetns pet tutor
Jada also estimates the perimeter of her garden by rounding the length and width to the nearest tenth. Which equation shows this estimate?
A. 12.6 + 3.2 + 12.6 + 3.2 = 31.6 meters
B. 12.6 + 3.3 + 12.6 + 3.3 = 31.8 meters
C. 12.5 + 3.5 + 12.5 + 3.5 = 32 meters
D. 12.7 + 3.3 + 12.7 + 3.3 = 32 meters
Answers
Answer:
B
Step-by-step explanation:
According to Albert Einstein (one of the smartest person) and Jeff Bezos (the richest person on earth)...the answer is B and will always be B ;0.
Find the function that represents the relationship on the chart
Answers
Answer:
last one f(x) = 7x-5
Step-by-step explanation:
7(0)-5 = -5
7(1)-5 = 2
7(2) - 5 = 9
...
Solve for x
x(6x+1)= 2
Answers
Answer:
x=1/2,-2/3
Step-by-step explanation:
Answer:
- 1/2 I would show my work but its too long sry
Step-by-step explanation:
ANSWER THIS ASAP PLS!!!
Solve for x.
A) -11
B) -12
C) -6
D) 11
Answers
Answer:
its A, B, C, or D
Step-by-step explanation:
hi what’s
0 divid. Ed bye o9sskwnqzjsmmskmsmskq?
Answers
PLZ HELP ME I WIlL GIVe U BRAINLIESt I BEGggg u HELp Me
What slope of the line on the graph
Answers
Answer:
6/3
Step-by-step explanation:
Answer:
slope is -2
equation for the line is y = -2x
Step-by-step explanation:
slope is rise over run
the rise is that the line goes down 2 units for every 1 unit it moves right
15.eye color if 2/3 of the girls in class have Brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class heither blue or brown eyes?
Answers
Answer:
Brown would be it
Step-by-step explanation:
Which shows the correct solution to the inequality To 21 +22
10
218 +p
7
10
5
-
1
-1
28 25
40 40
2p
3
ps-1
40
7 5
10
21+
7
-1
10
g+p
28 25
- 1
40
40 20
02-13
Mark this and return
Ne
SE
Answers
Answer:
C
Step-by-step explanation:
the answer is C !!!!!!!!!!!!!!!
Evaluate the expression 2/3 x−12 if x=18
Answers
Answer:
Step-by-step explanation:
Given equation is 2/3 x−12
Given x=18
Putting X=18 in given equation we get
2/3x-12= 2x18/3-12=
=12-12 =0 is the answer
pls help part 1 Evaluate: [tex]-5^{2}[/tex]
A. -25
B. 25
C. -10
D. 10
Answers
The supermarket has 48 aisles. 12 of the aisles are empty. What percentage of the aisles are empty
Answers
Answer:
25% of the isles are empty
Step-by-step explanation:
48/12 is 25%
Answer:
25%
Step-by-step explanation:
12 + 12 + 12 + 12= 48
if 12 isles are empty, then that is 1/4 of 48 aka 25%
Find the missing number in the following proportions. 20 : 40 :: d : 30
Answers
9514 1404 393
Answer:
15
Step-by-step explanation:
The proportion can be written as fractions:
[tex]\dfrac{20}{40}=\dfrac{d}{30}\\\\\dfrac{600}{40}=d\qquad\text{multiply by 30}\\\\\boxed{d=15}\qquad\text{finish the computation}[/tex]
Answer:
Step-by-step explanation:
Given
proportions. 20 : 40 :: d : 30
20/40=d/30
d=20×30/40
d=30/2
d=15.
What is the value of b? b+40 b+880 b-199
Answers
Answer:
921b-199
Step-by-step explanation:
plz help i don’t understand at all