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
Answer all of these
18% of 34
27% of 81
85% of 74
54% of 90
33% of 360
TOPIC
62% of 75
4% of 56
6% of 140
© 12% of 625
5% of 134
Finding a Percent of a
90% of 44
9% of 17
48% of 20
70% of 69
2% of 800
Some doctors recommend that no more than 30% of a
person's daily calones come from fats. Following this
recommendation. If you eat 2,400 calones in a day, what
is the maximum number that should come from fats?
When training for a fight Rocky tries to maintain a heart
rate that is 80% of his maximum heart rate, Rocky has a
resting heart rate of 60 and a maximum heart rate of
175 beats per minute. What is his training heart rate?
mbe
Answers
Answer:
18% of 34 = 6.1227% of 81 = 21.8785% of 74 = 62.954% of 90 = 48.633% of 360 = 118.862% of 75 = 46.54% of 56 = 2.246% of 140 = 8.412% of 625 = 755% of 134 = 6.790% of 44 = 39.69% of 17 = 1.5348% of 20 = 9.670% of 69 = 48.32% of 800 = 16-------------------------------------
30% of 2400 = 720 calories--------------------------------------
80% of 175 = 140 beats per minuteMr. and Mrs. Brown went to two movies. The first one lasted 3 1/2 hours and the second one lasted 1 1/3 hours . How much longer was the first than the second movie?
Answers
Answer:
2 1/6 longer
Step-by-step explanation:
3 1/2-1 1/3
7/2 - 4/3
21/6-8/6
13/6 or 2 1/6
so 2 1/6 longer.
Hope this helps :D
Answer:
2 1/6 hours longer
Step-by-step explanation:
Hope the helps!
In equilateral triangle ABC above, y =
(A) 40
(B) 60
(C) 70
(D) 75
(E) 80
Answers
Answer:
60°
Step-by-step explanation:
In an equilateral triangle all sides are equal so as all angles are same,
3 sided fig. 180÷3= 60°
Convert Repeating Decimal to Fraction
Convert the repeating decimal to a rational number.
ITEM BANK: Move to Bottom
4936/990
530/900
4311/9900
8099/990
674/990
0.4354 drag and din answer har
0.58 drag and drop wether
0.680 - drag and drop shower bord
4.985 - drag and drop antworten
8.180ding and dan wel
Answers
Step-by-step explanation:
0.345454...... = 4311/9900
0.5888..... = 530/900
0.68080..... = 674/990
4.98585..... = 4936/990
8.18080...... = 8099/990
please show work i would appreciate it
Answers
Answer:
a) x = 14
b) The perimeter of △QRS is 77 units.
Step-by-step explanation:
a) Due to the question asking for a solution using the Triangle Proportionality Theorem, it is assumed that △RQS is similar to the smaller triangle inside it.
Let us define the point at which the line inside △RQS meets line RQ as T, and the point at which that same line meets line RS as V.
Hence, △RTV ~ △RQS.
According to the Triangle Proportionality Theorem:
[tex]\frac{RT}{RQ} = \frac{TV}{QS} = \frac{VR}{SR}[/tex]
Hence, we can substitute all values that we know from the diagram:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{TV}{17} = \frac{21 - 7}{21}[/tex]
After getting this information, all we have to do is simplify and solve the equation:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{21 - 7}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{14}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{2}{3}[/tex]
[tex]3(2x - 2) = 2(2x + 11)[/tex]
[tex]6x - 6 = 4x + 22[/tex]
[tex]6x - 4x = 22 + 6[/tex]
[tex]2x = 28[/tex]
[tex]x = 14[/tex]
To verify this answer, we can plug in the value of x into the equation:
[tex]\frac{2(14) - 2}{2(14) - 2 + 13} = \frac{2}{3}[/tex]
[tex]\frac{26}{39} = \frac{2}{3}[/tex]
[tex]\frac{2}{3} = \frac{2}{3}[/tex]
Hence, after verification, we can get the answer: x = 14.
--------------------------------------------------------------------------------------------------------------
b) To find the perimeter of △QRS, all we have to do is to add all the lengths of the sides of △QRS together.
Hence, 2(14) - 2 + 13 + 17 + 21
= 28 - 2 + 13 + 17 + 21
= 77 units
Therefore, the perimeter of △QRS is 77 units.
Hope this helped!
your statement balance is 600.00 You have an outstanding checks for
125.00 and 175.00. an outstanding debit for 200.00. You also have an
outstanding deposit of 400.00. What is your adjusted balance? *
A.575.00
B.500.00
C.400.00
D.625.00
Answers
Answer:
B
Step-by-step explanation:
600+125+175=900-400(deposit)=500
or
600-125-175-300-200=100+400=500
Brainliest Please :)
Which number line best represents the solutions to 7 < -2x + 3?
Answers
Answer:
B or D
Step-by-step explanation:
PLZ ANSWER IF U KNOW THE ANSWER
Answers
Plz help
f(x)=2x+1 Find f(3)
Answers
Step-by-step explanation:
f(3)=2(3)+1
6+1
7
answer is 7
Answer:
f(3)=15
Step-by-step explanation:
just put 3 instead of x
what is the answer to 5/6 x 4/3
Answers
Answer: 5/6 * 4/3 = 10/9
The Decimal Would Be: 1.111111
Step-by-step explanation:
whats 0.1 as a percent
Answers
Answer:
TO findt he percent move the decimal place to the right 2 times. THis applies for any decimal. Therefore the percent is 0.1--->10%
Step-by-step explanation:
the diagonal of a square is 3√2 then find its length
Answers
hope that this answer helps you.
Slope for (-5,-1) (5,0)
Answers
Answer:
(0-(-1))/(5-(-5)) = 1/10
The inequality x S-8 would represent which of the following values?
Answers
A survey of us adults found that 11% think that congress is a good reflection of american views. you rnadomly select 35 us adults and ask them whether they think tha tocngress is a good reflection of american views.
Find the probability that the number who say yes is (a) exactly 8, (b) at least 10, and (c) less than 5, and (d) identify any unusual events. Explain.
Answers
Answer:
C) Less than 5
Step-by-step explanation:
First you find 11% of 35
35 x .11 = 3.85
3.85<5
Therefor- it's less than five. No idea if that was the question but uh- that's what I understood from it. TwT
A triangular flag has 2 sides with lengths 2 x and 1 side with length x.
A flag is the shape of an isosceles triangle, with two equal sides and a base. Sara has enough fabric to make a flag with a perimeter of 46.8 cm. She knows the flag needs a base that is half the distance of one of the sides.
What is the base of the largest triangular flag Sara can make?
cm.
Answers
Step-by-step explanation:
Perimeter = x + 2x + 2x = 5x
Since 5x <= 46.8cm, x <= 9.36cm.
The largest base is 9.36cm.
Answer:
9.36 is correct
Step-by-step explanation:
Help me out hereeeeeeeeeeeeeeeeee
Answers
Answer: The answer would be the 2nd choice. 2 4/5 is the answer. Step by-step explanation:
For 1 miles distance : 7/10 of a mile she runs and 3/10 she walks.
For 4 miles distance:(4 times the previous distance) she will run:
4*(7/10)= 18/20 = 2.8
2.8 as a mixed number/fraction is 2 4/5 therefore the answer is 2 4/5.
✨help✨
Madonna loves records. She has 338 of them. Her grand father gives her some for her birthday. She ends up with 456 after her birthday. At what percent did her grandfather give her. (I know it's a funky question. You have to divide the amount and then round it to the nearest hundred)
Answers
Answer:
34.9%Step-by-step explanation:
Ok, we need to express this number as a percent of increase. So, what we'll do is write this as a proportion.
456/338 = x/100
456 x 100 = 338x
45600 = 338x
x = 134.911242604
A 34.9% increase
Answer:
17.53%Step-by-step explanation:
Initial number = 388Final number = 456Increase in number:
456 - 388 = 68Increase in percent:
68/388*100% = 17.53% rounded to the nearest hundredsTim ate 12 buffalo wings. Jeff ate 125% of the amount Tim ate. How many wings did Jeff eat?
Answers
Answer:
%50
Step-by-step explanation:
hope this helped luv!
Theresa and her mother made homemade salsa. They made 4.5 quarts of salsa. They are going to store the salsa in pint-sized jars.
Calculate how many pint-sized jars Theresa will need to store 4.5 quarts to pints.
O 5 jars
O 6.5 jars
09 jars
O 12 jars
Answers
Answer:
9 pint sized jars
Step-by-step explanation:
There are two pints to the quart. 2x4=8, so there is 8 pints per 4 quarts. If one pint is the same as half a quart, we can write a pint as 0.5 quarts. So, there are 9 pints to 4.5 quarts.
Answer:
9 jars
Step-by-step explanation:
there are 2 pints in a quart so 4.5x2=9
Which of the following is an arithmetic sequence?
O A. 2, 4, 16, 32,
O B. 5,-5, 5, -5,..
OC. 2,3, 7, 1, ..
OD. 3, 0, -3, -6
Answers
Answer:
D
Step-by-step explanation:
because it has a varying and uniform difference of -3
When Margie visited the beach at Key West, she collected 50 seashells. She had 15
smooth shells and 35 shells with ridges. What percent of her shells had ridges?
35
30
70
65
Answers
Answer:
70
Step-by-step explanation:
Suppose a country's population at any time t grows in accordance with the rule dP dt = kP + I where P denotes the population at any time t, k is a positive constant reflecting the natural growth rate of the population, and I is a constant giving the (constant) rate of immigration into the country. If the total population of the country at time t = 0 is P0, find an expression for the population at any time t.
Answers
Answer:
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Step-by-step explanation:
Given that:
A country population at any given time (t) is:
[tex]\dfrac{dP}{dt}= kP+I[/tex]
where;
P = population at any time t
k = positive constant
I = constant rate of immigration into the country.
Using the method of separation of the variable;
[tex]\dfrac{dP}{kP+1}= dt[/tex]
Taking integration on both sides:
[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]
[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]
[tex]log (kP + I) =k t+kc_1[/tex]
By applying the exponential on both sides;
[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]
[tex]KP+I = e^{kt} *e^{kc_1}[/tex]
Assume [tex]e^{kc_1 }= C[/tex]
Then:
[tex]kP + I = Ce^{kt}[/tex]
[tex]kP = Ce^{kt}-I[/tex]
[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]
When time t = 0, The Total population of the country is also [tex]P_o[/tex]
[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]
[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]
[tex]P_o = \dfrac{C-I}{k}[/tex]
C - I = kP₀
C = kP₀ + I
Substituting the value of C back into equation(1), we have:
[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]
[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Please help fast, thanks.
Answers
help me ples 20 point
Answers
Answer:
40%
Step-by-step explanation:
6/15 * 100 = 0.4 * 100 = 40%
Answer:
40% of the pieces of fruit in the Bowl are apples.
Step-by-step explanation:
Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.
Total number of pieces of fruit in a bowl = 15 pieces
Number of pieces of apple in a bowl = 6 pieces.
Therefore, 40% of the pieces of fruit in the Bowl are apples.
34 divided by 523.6
Answer
Answers
Answer:
0.06493506493
Step-by-step explanation:
Answer:
0.064935065
Step-by-step explanation:
50+50+90+90=its a total of=
Answers
Answer:
280
Step-by-step explanation:
50+50=100 plus 90+90= 180 so 180+100=280
[IMAGE] please help me with 1, 2, and 3
Answers
Answer:
1. 5n + 10d = 90
2. (18,0)
3. (0,9)
What is the measure of angle Y?
60 40
Answers
Answer:
if it is triangle it is 80
In a random sample of 300 people in a town, 193 were female. What is the sample portion of female
Answers
Answer: 0.643
Step-by-step explanation:
There are 300 people and 193 were female.
The sample portion that is female is therefore;
= 193/300
= 0.643