Find the exact values of the six trigonometric ratios of the angle in the triangle 160 and 164
Answers
Answer:
[tex]\sin \theta = \frac{40}{41}[/tex], [tex]\cos \theta = \frac{3}{82}[/tex], [tex]\tan \theta = \frac{80}{3}[/tex], [tex]\cot \theta = \frac{3}{80}[/tex], [tex]\sec \theta = \frac{82}{3}[/tex], [tex]\csc \theta = \frac{41}{40}[/tex]
Step-by-step explanation:
We notice that figure represents a right triangle, the hypotenuse has a length of 164 units and the leg opposite to [tex]\theta[/tex] has a length of 160 units. The sine of [tex]\theta[/tex] is:
[tex]\sin \theta = \frac{160}{164}[/tex]
[tex]\sin \theta = \frac{40}{41}[/tex]
The leg adjacent to [tex]\theta[/tex] is determine by the Pythagorean Theorem:
[tex]r = \sqrt{164^{2}-160^{2}}[/tex]
[tex]r = 6[/tex]
Then, the cosine of [tex]\theta[/tex] is:
[tex]\cos \theta = \frac{6}{164}[/tex]
[tex]\cos \theta = \frac{3}{82}[/tex]
Lastly, we determine the remaining trigonometric ratios by using these identities:
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (1)
[tex]\cot \theta = \frac{1}{\tan \theta}[/tex] (2)
[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (3)
[tex]\csc \theta = \frac{1}{\sin \theta}[/tex] (4)
If we know that [tex]\sin \theta = \frac{40}{41}[/tex] and [tex]\cos \theta = \frac{3}{82}[/tex], then the trigonometric ratios are, respectively:
[tex]\tan \theta = \frac{\frac{40}{41} }{\frac{3}{82} }[/tex]
[tex]\tan \theta = \frac{80}{3}[/tex]
[tex]\cot \theta = \frac{1}{\frac{80}{3} }[/tex]
[tex]\cot \theta = \frac{3}{80}[/tex]
[tex]\sec \theta = \frac{1}{\frac{3}{82} }[/tex]
[tex]\sec \theta = \frac{82}{3}[/tex]
[tex]\csc \theta = \frac{1}{\frac{40}{41} }[/tex]
[tex]\csc \theta = \frac{41}{40}[/tex]
Related Questions
what is the correct factorization of x^2 - 2x - 15?
Answers
Answer:
Step-by-step explanation:
x2 - 2x - 15
x2 - 5x + 3x - 15
x(x - 5) + 3(x - 5)
(x - 5) and (x + 3) are the factors
if this needs to be solved further, you will need to set both of these equations equal to 0.
x-5=0 and x+3=0
this will give you x=5 and x=-3
i hope this helped :)
convert 53 yards per hour into inches per day
Answers
1 yard = 36 inches.
53 yards per hour x 36 inches per yard = 1908 inches per hour.
1 day = 24 hours.
1908 inches per hour x 24 hours = 45,792 inches per day.
A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school diploma is 0.87. a)Suppose you took a simple random sample of 100 young Americans. We know because of sampling variability that the sample proportion of those who earned a high school diploma would vary each time you took a sample. Assuming the value above can be taken as the population proportion (i.e. as a parameter), what model can be used to describe how these sample proportions would vary
Answers
Answer:
normal distribution can be used to model the sample proportions
Step-by-step explanation:
N ( sample size ) = 100
probability of earning high school diploma (p) = 0.87
probability of not earning high school diploma ( q ) = 0.13
hence ;
∈( P ) = p = 0.87
Var ( p ) = [tex]\frac{pq}{n}[/tex] = [tex]\frac{0.86 * 0.13 }{100}[/tex] = 0.001131
therefore ; p ~ N = ( 0.87 , 0.001131 )
1/6 foot = how many inches
please help if you have the right answer
Answers
Answer: 2 inches
Step-by-step explanation:
1 foot=12 inches
1/6=1/6 foot
12/6=2 inches in 1/6 foot
Lauren saves 30% of her paycheck to purchase the iPhone 12. She earns $325 per paycheck. How much will Lauren have for her iPhone if she has saved from the first 2 paychecks
PLS HELP
Answers
Answer:
She will have saved $195
Step-by-step explanation:
If we had her two paychecks together she will have saved $650.
30% of 650 = 195
We get this by taking 650 times .3
the cost for fudge at candy lane is represented by the table.the graph the cost for similar fudge that best fudge shop sell. a. the unit rate for fudge at candy lane to equal the unit rate at best fudge shop. B.the unite rate for fudge at best fudge shop is less than unit rate at candy lane. C.the unite rate for fudge at candy lane is less than the unit rate at best fudge shop. D cost 3 pounds of fudge at best fudge shop is less than the cost of a pound of fudge at sweet treats
Answers
Answer:
B
Step-by-step explanation:
The correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a table that shows the cost for fudge at candy lane. The graph represents the cost for similar fudge that best fudge shop sell.
The slope of straight line represented by the table -
m[1] = (16 - 8)/(2 - 1)
m[1] = 8
The slope of the line plotted on graph -
m[2] = (9 - 6)/(3 - 2)
m[2] = 3
The slope is the measure of unit rate. Therefore, the unit rate of best fudge is less than unit rate of candy cane.
The cost 3 pounds of fudge at best fudge shop = 3 x 3 = $9
The cost 1 pound of fudge at candy lane = $8
Hence, cost 3 pounds of fudge at best fudge shop is greater than the cost of a pound of fudge at sweet treats.
Therefore, the correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.
To solve more questions on straight line graphs, visit the link below-
brainly.com/question/2954112
#SPJ6
[Refer to the image attached for table and graph]
HELP PLEASE!!
What is Y
Answers
Can someone help with this Problem? It is about Evaluating expressions using properties of exponents. Would help a lot. Attachment below
Answers
9514 1404 393
Answer:
1/192
Step-by-step explanation:
The properties of exponents useful here are ...
a^0 = 1 . . . . for a ≠ 0
a^-b = 1/a^b
__
[tex]4^{-2}\cdot 12^{-1}\cdot 12^0=\dfrac{1}{4^2}\cdot\dfrac{1}{12}\cdot 1\\\\=\dfrac{1}{16\cdot12}=\boxed{\dfrac{1}{192}}[/tex]
What is the equation relating x and
y together?
y
1
2
3
4
5
25
23
21
19
17
y=-2x + [?]
Answers
Answer:
ommmm I have no idea Butt 1 of my fav numb is 17 so pick that
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Using the empirical rule, determine the interval that would represent the middle 95% of IQ scores.
Answers
Answer:
About 95% of individuals have IQ scores in the interval 100 ± 2 ( 15 ) = [ 70 , 130 ] .
Step-by-step explanation:
hope this helps
A group of students are standing in rows. There are as many students in a row as there are rows. If there are 64 students in the group, how many students are standing in pach row?
A. 4
B 6
C. 8
D 12.
Answers
Answer:
B..im pretty sure
Step-by-step explanation:
First it cant be D because 12 x __ = 64. There is no whole number multiplied by 12 that equals 64. So cross that out. then it's not B because 6 x ___ = 64. So also cross that out. the only thing u have left is 4 and 8. Then u can cross out A because the group of students has to be the same number of rows. Which is 8 x 8 aka B. The answer is B
Answer:
B
Step-by-step explanation:
How do you rotate triangle A",B",C" 270 degrees around the origin. coordinates A" (-1,1), B"(1,-2) and C"(0,-4)
Answers
9514 1404 393
Answer:
rotated vertices are (1, 1), (-2, -1), (-4, 0)
Step-by-step explanation:
When the rotation direction is not specified, it is usually taken to be counterclockwise. Rotation 270° CCW is the same as rotation 90° CW. The transformation of coordinates is ...
(x, y) ⇒ (y, -x)
Then your rotated points become ...
A(-1, 1) ⇒ A'(1, 1)
B(1, -2) ⇒ B'(-2, -1)
C(0, -4) ⇒ C'(-4, 0)
_____
In the attached, the rotated triangle is shown in red. As an example, the arc through which point C is rotated is shown.
I need help please and thanks
Answers
Answer:
68 degrees
Step-by-step explanation:
1 & 6 have to equal 180. Therefore, if 1 is 112 then you take 180-112. Then you get 68 degrees.
Answer:
Angle 6 would be 68 degrees
Step-by-step explanation:
Angles 1, 3, 5, and 7 all equal 112. you would subtract 112 from 180 to get the measurement for angles 2, 4, 6, and 8
Hurry please
I need the answer to this one in 2 minutes
Answers
Answer:
125
Step-by-step explanation:
45 ÷9=5
5² or 5×5=25
25×5=125
Hope this helps!
Answer:
I THINK ITS
Step-by-step explanation:
5x(2025 ÷81)
5x25
125
Merry Christmas please help
Answers
Happy holidays! Hope you have a great Christmas!
Answer:
All Of The Number At The Top
Step-by-step explanation:
Like Said, The Tables Functions f
So, Basically It's A Challenge,
All Of The Numbers In Row X From Above Table
I Hope You Found This Answer Helpful
Good Day
You'll Get 100% Don't Stress It✨
By: LocalLesMara
!!HELP!! What is q times 10?
Answers
Answer:
Q10. You just put them together because it's multiplying of a letter and a number
**I thought I answered this question yesterday, is this a deja vu or something**
The federal government would like to test the hypothesis that the average age of men filing for Social Security is higher than the average age of women with the following data: Men Women Sample mean 64.5 years 63.6 years Sample size 35 39 Population standard deviation 3.0 years 3.5 years If Population 1 is defined as men and Population 2 is defined as women, the 90% confidence interval for the difference in population means is (closest to) ________. Group of answer choices
Answers
Answer:
The 90% confidence interval is [tex] -0.3433< \mu_1 - \mu_2 < 2.1433[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean for men is [tex]\= x_1 = 64.5 \ years[/tex]
The sample mean for women is [tex]\= x_2 = 63.6 \ years[/tex]
The sample size for men is [tex]n_1 = 35[/tex]
The sample size for women is [tex]n_2 = 39[/tex]
The standard deviation for men is [tex]s_1 = 3.0[/tex]
The standard deviation for women is [tex]s_2 = 3.5[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645 [/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{s_1^2 }{n_1} + \frac{s_2^2}{n_2} }[/tex]
=> [tex]SE = \sqrt{\frac{3^2 }{35} + \frac{3.5^2}{39} }[/tex]
=> [tex]SE = 0.7558[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
=> [tex]E = 1.645 * 0.7558[/tex]
=> [tex]E = 1.2433[/tex]
Generally 90% confidence interval is mathematically represented as
[tex](\= x_1 - \= x_2) -E < \mu_1 - \mu_2 < (\= x_1 - \= x_2) -E [/tex]
=> [tex](64.5 - 63.6) -1.2433< \mu_1 - \mu_2 <(64.5 - 63.6) +1.2433[/tex]
=> [tex] -0.3433< \mu_1 - \mu_2 < 2.1433[/tex]
Grade 4 Mathematics- Checkpoint #3
In 2008 the total number of cell phone users in Indonesia was about 140,578,000. Which expression has the same value as 140,578,000?
Answers
Answer:
2^4 x 5^3 x 70289
Step-by-step explanation:
16 x 125 x 70289=140,578,000
do you know the answer
Answers
Answer:
The answer is 15.
Other:
Brainliest? Thanks!
3.5x + 4y if x=3 and y = 7
4 6x-42 if x =4 and 2
5.83 +4 ry if y=2 and y= 100
Answers
3,5× 3 + 4 × 7 =3 8,5
46*4-42=143 46* 2- 4 2= 50
5,83+4*2=13,83 5,83+4*100=405,83
pweese help!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
How is the space between consecutive whole numbers divided on the number line?
O into halves
O into fifths
O into sixths
O into sevenths
Answers
C. INTO SIXTHS
I LITRALLY JUST TOOK THE TEST ON EDGE. SO YOU CAN TAKE MY WORD FOR IT
I HOPE I WASNT TOO LATE. IF I WAS, SORRY
The number of grids or intervals on the given number line between any two consecutive whole numbers is six thus option (C) is correct.
What is a number line?In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
A horizontal number line is the most common representation and can be extended infinitely in any direction.
As per the given number line,
Since 1 is a whole number and 2 is also a whole number.
The number of intervals between 1 and 2 is 6.
Thus, between consecutive whole numbers divided on the number line is 6.
Hence "The number of grids or intervals on the given number line between any two consecutive whole numbers is six".
To learn more about the number line,
https://brainly.com/question/13189025
#SPJ2
If 12 cookies cost $3 how much would it be for 9 cookies
Answers
12:3
9:x
x is how much it would cost. so try to find x.
x= 2.25
9 cookies cost 2 dollars and 25 cents
can someone help me with this
Answers
I hope this helps.
Answer:0.98
hope this helps have a good day
Step-by-step explanation:
Casey walked 2.1 miles to the grocery store. She then walked 0.5 miles to the post office and 0.8 miles to work. How far did she walk in total? Convert your answer into kilometers.
Answers
Answer:
3.4 miles and 5.472 kilometers
Someone please help look at the picture please anything would help
Answers
y = -8x – 3
x+y=7
Is (3, 4) a solution of the system?
Answers
4 = -24-3 false
3 + 4 = 7 true
The first one is false, second is true
Answer: the answer is no :)
Anyone can answer?? if u can thank u soooo much it means the world to me
Answers
Answer:
Tulips• 7, 14, 21, 28 and 35.
Carnations• 3, 6, 9, 12 and 15.
Other:
Find above the whole number ratio for the tulips and carnations graph. Brainliest? Thanks!
(4,8), m=5 need a step by step answer please
Answers
Answer:
8=4x+5
Step-by-step explanation:
Slope-intercept form: y=mx+b
1. Identify your terms:
x: 4
y:8
b/slope: 5
2. Solution:
8=4x+5
Find the zero of the function.
f(x)= 4x^2– 12x+9
Answers
Answer:
The zero is x = 3/2 = 1.5
Step-by-step explanation:
We recognize that the trinomial 4 x^2 - 12 x + 9 is a perfect square trinomial, which comes from the following squared binomial:
(2 x - 3)^2
Therefore, the zeros are the x-values that verify the following:
(2 x - 3)^2= 0
that is (2 x - 3) = 0 and solving for "x":
2 x = 3
x = 3 / 2
x = 1.5