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
degree of precision 15.68 x 1.1
Answers
Answer:
15.68×1.1 = 17.248 so if we see then it has 5 sig figs
2. A spider can walk at a certain speed and run at
another speed. If she walks for 10 seconds and runs for 9
seconds, she travels 85m. If she walks for 30 seconds and
runs for 2 seconds, she travels 130m. Find her speeds of
walking and running.
Answers
Answer:
The answer is below
Step-by-step explanation:
Speed is the ratio of distance covered to the time taken. Speed is given by the formula:
speed = distance / time.
Let us assume the spider walking speed is x and its running speed is y.
If the spider walks for 10 seconds and runs for 9 seconds, she travels 85m. distance = speed * time, hence:
Total distance = distance covered walking + distance covered running
10x + 9y = 85 (1)
Also if she walks for 30 seconds and runs for 2 seconds, she travels 130m. Hence:
30x + 2y = 130 (2)
Solving equation 1 and 2 simultaneously by mutiplying equation 1 by 3 and subtracting equation 2 from the result:
25y = 125
y =5 m/s
Put y = 5 in eqn. 2
30x + 2(5) = 130
30x = 120
x = 4 m/s
The spider walks at 4 m/s and runs at 5 m/s
If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)
Answers
Answer:
C. G' (4,-7), R' (2,-3), T'(6,-4)
Step-by-step explanation:
Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.
A sporting goods store is selling all their exercise equipment for 30% off.
The regular price for an exercise bicycle is $260. The regular price for a set of hand weights is $120.
Part A
Use the drop‐down menus to explain how to find the sale price of the exercise bicycle.
Find ____________ of the cost of the exercise bicycle. Multiply that amount by
_______
to find 30% of the cost. Then (x-+/ choose 1)
the regular price to find the sale price.
Part B
Use your answers from Part A to find the sale price for the exercise bicycle. Enter your answer in the line
$_______
Part C
What is the sale price of the hand weights?
$114
$84
$36
$380
Answers
Answer:
weird
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
answered it. but I really need the answer tho like rn!
Estimate the square root of 296 to the nearest tenth.
Answers
Answer:
17.2
Step-by-step explanation:
Answer:
±17.20
Step-by-step explanation:
Follow Me Please
pls help me with the math test will give the first person who answers brainliest answers and points
write the expression for 100 less than the sum of 3 and x
Answers
Answer:
3 + x < 100
3 + x - 3 < 100 - 3
x < 97
Step-by-step explanation:
Which is greater 0.25 or 0.025
Answers
Answer:
0.25
Step-by-step explanation:
0.25*100=25
0.05*100=5.25
25 is greater than 5.25 so 0.25 is your answer
Hope this helps :) and pls give brainliest
helpppppp pleaseeee
question: Why do we need to know the mass of a robot? *
why is this in math why does my teacher does this
Answers
Answer:
To know what the answer is
Step-by-step explanation:
clearly I do not know, but I can say that we do need to know the mass bc in the future there will be more and more androids on the rising making human interaction bad.
to find out the equation take the seed and the time. (this to make it look like i answered) Taking the mass you will be able to find out how manyspeed is found by the time and masstime is found out by the mass and speedi dont know if this helpedAnswer:
Step-by-step explanation:
Solve kx - 3 = 5 for x.
A. x = 8 - k
B. x = 8k
C. x=2/k
D. x= 8/k
Answers
Answer: D
Step-by-step explanation:
I just got it wrong and D was the answer
nodadnotoday is my Spotify tho
GIVING BRAINLIEST AND STARS
13)
Using a map scale of 1/2 inch = 10 miles, what would be the distance on the map between two cities that are actually 120 miles
apart?
A)
6 inches
B)
8 inches
C)
10 inches
D)
12 inches
Answers
Answer:
A) 6 Inches
Step-by-step explanation:
1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.
Conversion rate is 120 ÷ 10 which equals 12.
Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.
i'd appreciate a brainliest :)
HELP WILL GIVE BRAINLIEST IF CORRECT
Answers
Answer:
hiii
your answer is option c
HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN
Each of four test scores in Connie’s class is to be weighted equally. On the first three tests, Connie scored 80%, 90% and 95%. What percent must she score on her fourth test to have an overall average of exactly 90%?
Answers
Answer:
95%is the answer
Step-by-step explanation:
Answer:
95%
Step-by-step explanation:
We can use the balancing method to do this.. first what is the total below 90?
The total is 10% because 90-80 which was the only percentage below 90 is 10%. Then, what is the total above 90?
The total is 5% because the only percentage above 90 is 95 and 95-90 is 5%
Now we use the balancing method to get from 5-10.
Using the balancing method we get 95%
Multiply. Write the answer in simplest form.
2 1/6 x 3 1/2
Answers
Answer:
The answer is 91/12 in simplest form.
which expression is not equivelent to 2/3 x 4
Answers
Answer:
8/3Step-by-step explanation:
[tex]\frac{2}{3} \times 4\\\\\mathrm{Apply\:the\:fraction\:rule}:\\\quad \frac{a}{b}\times c=\frac{a\times c}{b}\\\\\frac{2}{3}\times \:4=\frac{2\times \:4}{3}\\\\\mathrm{Multiply\:the\:numbers:}\:\\2\times \:4=8\\\\=\frac{8}{3}[/tex]
Solve P-6 = 16. Check your answer.
O p = 22
O p = -22
O p = 10
O p = -10
Answers
P-6=16
we can add 6 to both sides to cancel out the -6 and get p by itself.
p=16+6
now we add them
p=22
-2(x+4)²= -200
can you guys please help
Answers
I don't understand how to do things like 5 divided by 1/3.
Answers
No worries
First write 5 as 5/1.
Then, our division becomes:
5/1 ÷ 1/3
Then we just need to turn on second number upside down and multiply.
5/1 × 3/1
= 15/1
=> 15
Since I’m kinda slow I need help on this please
Answers
Answer:
when x=5, y=20
when x=3, y=12
when x=4, y=16
I hope that helps you!! :)
Riz got $200 for his birthday. He bought several long tennis rackets that cost $45.50 each. After the purchase he has $18 . Write an equation to find out how many rackets he bought and then find the number of rackets.
Answers
Answer:
he has bought 18 rackets.
Step-by-step explanation
papa loves a big juicy peen inside of him
Answer:
4
Step-by-step explanation:
(200-18)/45.50
= 182/45.50
= 4
What is the answer answer and plz give me step by step explaining
Answers
Answer:
x = 5
Step-by-step explanation:
6 + 8(x - 1) = 2(3x + 4)
We evaluate the numbers in the brackets first.
(8 × x = 8x, 8 × 1 = 8, 2 × 3x = 6x, 2 × 4 = 8)
6 + 8x - 8 = 6x + 8
The left hand side of the equation is not exactly simplified, so we will evaluate it further first.
(6 - 8 = -2)
8x - 2 = 6x + 8
Now we can start shifting the x and the numbers separately.
Note that when pushing 6x from the right side to the left side, it needs to change to a negative 6x and vice versa for -2 turning into +2.
8x - 6x = 8 + 2
Further evaluation
2x = 10
Now we can simply find x.
Note that for this, ×2 becomes ÷2 when it shifts from the left side to the right side of the equation.
x = 10 ÷ 2
Evaluate.
x = 5
What is the approximate area of the unshaded region in the figure below
Answers
Answer:
where is the shaded part?
Step-by-step explanation:
Answer: We can't answer the question without a shape or an expatiation. Please try again with an image or at least tell the answers and image in detail.
Step-by-step explanation:
solve for the missing value (?) 3:9=? ?:81=
Answers
Answer:
27
Step-by-step explanation:
First you need to figure out what times 9 = 81
9 x 9 =81
since you have to do the same thing on both sides of the equation you do
3 x 9
which gets you 27
Brooke measures the height of her bean plant for a science project. The bean plant is 12.5 inches tall.
How many centimeters tall is Brooke’s bean plant?
Answers
Answer:
its 31.75
Step-by-step explanation:
12.5 inch = 31.75 cm
In how many ways can the letter of word number taken two at a time
Answers
Answer:
So the number of ways of choosing two distinct letters at a time is (42)=6. We can then add the duplicate pairs which are O,O and N,N to give a total of 8 possible pairs.
Answer:
15
Step-by-step explanation:
There are 6 letters in the word number
This is 6 choose 2
This is a combination
The formula is 6! / ( 2! * (6-2)! )
6! / 2! 4!
(6*5*4*3*2*1) / ( 2*1 * 4*3*2*1)
Canceling like factors
(6*5) / ( 2*1)
30/2
15
There are 15 possible ways to have 6 choose 2
Is this a function?
Answers
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
In my opinion I would say No but I could be wrong
What is Square root of 296 to the nearest tenth?
Answers
Answer:
16.4
Step-by-step explanation:
√269= 16.40121946...
simplifies to 16.4 I believe
Answer: 17.2
Step by step explanation: Here are step-by-step instructions for how to get the square root of 296 to the nearest tenth:
Step 1: Calculate
We calculate the square root of 296 to be:
√296 = 17.20465053408530
Step 2: Reduce
Reduce the tail of the answer above to two numbers after the decimal point:
17.20
Step 3: Round 17.20 so you only have one digit after the decimal point to get the answer:
17.2
Write fifty three hundredths in standard form
Answers
Answer:
53/100 or 0.53 i think thats right
Which of the following is not a solution of the equation y=3x-4?
A. 2,2
B. 0,-4
C. 4,8
D. -1,-1
Answers
2 = 3(2) - 4, true
-4 = 3(0) - 4, true
8 = 3(4) - 4, true
-1 = 3(-1) - 4, false
Solution: D
HELP ME PLES I NEED IT
Answers
Percentage of 70% of what = 35?
70% × ? = 35
? =
35 ÷ 70% =
35 ÷ (70 ÷ 100) =
(100 × 35) ÷ 70 =
3,500 ÷ 70 =
50
Answer:
The trip is 50 miles
Step-by-step explanation:
30 = (60/100)T
T = (10/6)(30) = (5/3)(30) = 50 miles
Robin, who is self-employed, contributes $4500/year into a Keogh account. How much will he have in the account after 30 years if the account earns interest at the rate of 2.5%/year compounded yearly?
Answers
Answer:
The amount that would be in the account after 30 years is $368,353
Step-by-step explanation:
Here, we want to calculate the amount that will be present in the account after 30 years if the interest is compounded yearly
We proceed to use the formula below;
A = [P(1 + r)^t-1]/r
From the question;
P is the amount deposited yearly which is $4,500
r is the interest rate = 2.5% = 2.5/100 = 0.025
t is the number of years which is 30
Substituting these values into the equation, we have;
A = [4500(1 + 0.025)^30-1]/0.025
A = [4500(1.025)^29]/0.025
A = 368,353.3309607034
To the nearest whole dollars, this is;
$368,353