The tan θ and cos θ values of 17π/12 are illustrations of trigonometry ratios
The values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively
Part A: tan θ using the sum formulaWe have:
θ = 17π/12
Express as sum
θ = 9π/12 + 8π/12
Simplify
θ = 3π/4 + 2π/3
The above becomes
tan(17π/12) = tan(3π/4 + 2π/3)
Using the sum formula, we have:
tan(A + B) = [tan(A) + tan(B)]/[1 - tan(A)tan(B)]
Substitute known values
tan(3π/4 + 2π/3) = [tan(3π/4) + tan(2π/3)]/[1 - tan(3π/4)tan(2π/3)]
Evaluate the expression
tan(3π/4 + 2π/3) = [-1 - √3]/[1 - (-1)(-√3)]
Evaluate the product
tan(3π/4 + 2π/3) = [-1 - √3]/[1 - √3]
Rationalize
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-1 - \sqrt3}{1 - \sqrt3} * \frac{1 + \sqrt3}{1 + \sqrt3}[/tex]
Evaluate the product
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + \sqrt3)^2}{1 - 3}[/tex]
This gives
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + 3 + 2\sqrt 3)}{-2}[/tex]
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(4 + 2\sqrt 3)}{-2}[/tex]
Divide
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = 2 + \sqrt 3[/tex]
So, we have:
tan(17π/12) = 2 + √3
Part B: cos θ using the difference formula.We have:
θ = 17π/12
Express as difference
θ = 9π/4 - 5π/6
The above becomes
cos(17π/12) = cos(9π/4 - 5π/6)
Using the difference formula, we have:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
So, we have
cos(17π/12) = cos(9π/4)cos(5π/6) + sin(9π/4)sin(5π/6)
Evaluate
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} * - \frac{\sqrt 3}{2} + \frac{\sqrt 2}{2} * \frac 12[/tex]
Evaluate
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (- \frac{\sqrt 3}{2} + \frac 12)[/tex]
Evaluate the difference
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (\frac{1 - \sqrt 3}{2})[/tex]
Expand
cos(17π/12) = (√2 - √6)/4
Hence, the values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively
Read more about trigonometry ratios at:
https://brainly.com/question/11967894
help, Surface area of cubes and prisms
Answer:
2382
Step-by-step explanation:
You can use rectangle surface area= l × b
2×(27×21)+2×(27×13)+2×(21×13)
=2382
Figure 1
Figure 2
B
D
E
С
Z
128 cm
2
am
Area of Figure 1 =
Area of Figure 2 =
Perimeter of Figure 1 = 24 cm
Perimeter of Figure 2 = 21 cm
BC=
DE = 7 cm
Tip: Go to the internet and put the topic you are focused more on that you posted in Brainly
Step-by-step explanation:
Try it to give you some help
help plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
G. Between 6 and 7
Step-by-step explanation:
As 41 lies between the square of 6 and 7
James found a pair of shoes he wanted at two different stores. At store A they were $35 and he had a 20% off coupon. At store B they were $40 and he had a 30% off coupon. Both stores had 7% sales tax. Which would be the better deal, and by how much?
Answer: you gotta add
35+20 and that =55
55+30 and that =85
85+40 and that =125 the next step is
125+7 =132
Step-by-step explanation: hope this helps:)
What is 594 minus 236?
Answer:
358
Step-by-step explanation:
Help with all questions in pictures please
Just put the answers please (ex: 1A 2C 3B. etc)
For question number 7 where it says (Which of the following images represents the polar graph of r = 4cos 2θ?) only two of the graphs are shown please if you can include a graph of the correct answer *70Points*
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Convert point Q to polar coordinates (accounting for correct direction):
[tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(-5)^2+(-5\sqrt{3})^2}=\sqrt{25+75}=\sqrt{100}=10\\\\\theta=\tan^{-1}\biggr(\frac{-5\sqrt{3}}{-5}\biggr)=\tan^{-1}\bigr(\sqrt{3}\bigr)=\frac{4\pi}{3}[/tex]
Thus, the answer is [tex]\displaystyle \biggr(10,\frac{4\pi}{3}\biggr)[/tex], or A
Problem 2
Make polar substitutions:
[tex]x^2+y^2-2x+8y=0\\\\r^2-2r\cos\theta+8r\sin\theta=0\\\\r^2=2r\cos\theta-8r\sin\theta\\\\r=2\cos\theta-8\sin\theta\\\\r=-8\sin\theta+2\cos\theta[/tex]
Hence, the answer is C
Problem 3
Eliminate the parameter:
[tex]x=t+3\\x-3=t\\\\y=t^2+2t\\y=(x-3)^2+2(x-3)\\y=x^2-6x+9+2x-6\\y=x^2-4x+3[/tex]
Hence, the answer is C
Problem 4
Identify [tex]z_1[/tex] and [tex]z_2[/tex] and add the complex numbers:
[tex]z_1+z_2=(-3+5i)+(-5-2i)=-3+5i-5-2i=-8+3i[/tex]
Thus, the correct answer is S
Problem 5
Use the formula for multiplying complex numbers in polar form:
[tex]z_1z_2=r_1r_2(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2))\\z_1z_2=(5)(15)(\cos(240^\circ+135^\circ)+i\sin(240^\circ+135^\circ))\\z_1z_2=75(\cos375^\circ+i\sin375^\circ)\\z_1z_2=75(\cos15^\circ+i\sin15^\circ)[/tex]
Hence, the answer is A
Problem 6
Determine when the ball first hits the ground:
[tex]y=-\frac{1}{2}gt^2+(v\sin\theta)t+y_0\\0=-\frac{1}{2}(32)t^2+(58\sin19^\circ)t+1.9\\0=-16t^2+(58\sin19^\circ)t+1.9\\t\approx1.273[/tex]
Determine the horizontal distance covered by the ball:
[tex]x=(v\cos\theta)t\\x=(58\cos19^\circ)(1.273)\\x\approx69.811[/tex]
Hence, the best answer is C
Problem 7
The equation is in the form of [tex]r=a\cos(n\theta)[/tex] where [tex]a[/tex] is the length of each petal and the curve has a horizontal pole. If [tex]n[/tex] is odd, then there are [tex]n[/tex] petals, but if [tex]n[/tex] is even, then there are [tex]2n[/tex] petals.
From our given equation, there are clearly 4 petals since [tex]n[/tex] is even, and each petal length is 4 units. Hence, the first graph is correct.
am I right? please only answer if you are positive that you’re correct. thank you!
Answer:
yes you are correct :)))
What is the value of x?
[tex]\sin 30^{\circ} = \dfrac{LJ}{8\sqrt 2}\\\\\implies LJ = 8\sqrt 2 \sin 30^{\circ} =8\sqrt 2 \cdot \dfrac 12 = 4\sqrt 2\\\\ \text{Now,}\\\sin 45^{\circ} = \dfrac{LM}{LJ} \\\\\implies LM = \sin 45^{\circ} LJ\\\\\implies x = \dfrac 1{\sqrt 2} \cdot 4\sqrt 2 = 4 ~~ units.[/tex]
Answer:
x = 4
Explanation:
[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]
Solve for LJ:
[tex]\hookrightarrow \sf sin(30) = \dfrac{LJ}{8\sqrt{2} }[/tex]
[tex]\hookrightarrow \sf sin(30)*8\sqrt{2} ={LJ}[/tex]
[tex]\hookrightarrow \sf {LJ} = 4\sqrt{2}[/tex]
Solve for LM:
[tex]\hookrightarrow \sf \sf sin(45)= \dfrac{LM}{4\sqrt{2} }[/tex]
[tex]\hookrightarrow \sf \sf sin(45)*4\sqrt{2} = {LM}[/tex]
[tex]\hookrightarrow \sf {LM} = 4[/tex]
solve for x
plss help
Answer:
2
Step-by-step explanation:
These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.
The perimeters of two similar right triangles have a ratio of 3 to 5. If the height of the larger triangle is 12 meters, what is the height of the
smaller triangle?
Answer:
7.2 meters
Step-by-step explanation:
Similar triangles have linear dimensions that are proportional. The ratio of heights will be the same as the ratio of permeters:
h/(12 m) = 3/5 . . . . . . . small/large
h = (3/5)(12 m) = 7.2 m . . . . . . multiply by 12 m
The height of the smaller triangle is 7.2 meters.
PLEASE HELP!!!! ILL MARK BRAINLIEST WITH 10O POINTS!!!!!!! WITH EXLANATION!!
Use the diagram below to create a paragraph proof for the statement: "The sine and cosine of complementary angles are equal"
Answer:
Complemenraty angles are two angles with sum of 90°. In the given triangle ∠A and ∠B are complementary.
Now, the sine and cosine
sine = opposite side/hypotenusecosine = adjacent side/hypotenuseFind the sine of ∠A and cosine of ∠B
sin A = BC/ABcos B = BC/ABSince right sides are equal, left sides are equal too
sin A = cos BSimilarly, we can show that
sin B = cos AProved
A bag of balloons contains 4 red balloons, 11 green balloons, 15 yellow balloons, and 8 orange balloons. What is the probability that
a randomly selected balloon would be green or orange?
A. 23/38
B. 13/19
C. 15/38
D. 1/2
Answer:
D 1/2
Step-by-step explanation:
Probability is the ratio of the number of favorable outcomes to the total number of outcomes
number of favorable outcomes = 11+8 = 19
total number of outcomes = 38
The probability that a randomly selected balloon would be green or orange is
19/38 = 1/2
100 pts what is 2X2+6X5+8
Answer:
It's 42.
Step-by-step explanation:
Order of operations:
4+6*5+8
4+30+8
34+8
= 42
Therefore, the answer is 42.
Answer:
42
Step-by-step explanation:
. Carlee surveyed customers as they left a convenience store. She asked them, “How many items did you
purchase?” The results are shown in the line plot.
(a) How many customers were surveyed?
(b) What was the greatest number of items purchased by a customer?
(c) How many customers purchased 9 items?
(d) How many customers purchased at least 5 items?
(e) What was the median number of items purchased?
Answer:
We need the picture of the line plot in order to answer the question
Step-by-step explanation:
An 8-sided solid is labeled with faces 1, 2, 3, skip, 4, 5, 6, skip. What is the sample space for the number solid, and what is the probability of rolling a 1?
A.
{1,2,3,4,5,6,skip,skip}; P(1)=0.125
B.
{1,2,3,skip,4,5,6}; P(1)=0.14
C.
{1,2,3,4,5,6, skip}; P(1)=0.125
D.
{1,2,3,4,5,6}; P(1)=0.17
Using it's concepts, it is found that the sample space and the desired probability are given by:
C. {1,2,3,4,5,6,skip}; P(1)=0.125
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
If an outcome happens more than once, as is the case for the "skip" in this problem, it is shown only once on the sample space, hence for this problem it is given by:
{1,2,3,4,5,6, skip}
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, one out of eight outcomes result in a one, hence:
P(1) = 1/8 = 0.125.
Which means that option C is correct.
More can be learned about probabilities at https://brainly.com/question/14398287
If 12% of a number is 30, find 4% of that number.
12%= 30
-> 100%= 30÷12×100
-> 100%= 250
4% of 250
-> 4%=250÷100×4
-> 4%= 10
Bob is throwing a party. He has 222222 pints of soda. At the end of the party, there are 888 pints of soda.
How many cups of soda were drank during the party?
The number of the pints of soda were drank during the party will be 14 pints.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
Bob is throwing a party. He has 22 pints of soda.
At the end of the party, there are 8 pints of soda.
Then the number of the pints of soda were drank during the party will be
⇒ 22 – 8
⇒ 14
The number of the pints of soda were drank during the party will be 14 pints.
More about the subtraction link is given below.
https://brainly.com/question/4319655
#SPJ1
A spinner with 10 equally sized slices has 2 blue slices, 4 yellow slices, and 4 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a blue slice? Write your answer as a fraction in simplest form.
Answer:
1/5
Step-by-step explanation:
the number of all slices is 10.. and you got 2 blue ones
so you get 2/10 and if you simplify it you get 1/5
Find the median of the set of numbers below.
15, 16, 15, 7, 21, 18, 19, 20, 11
Answer :
16
Explanation :
You arrange the numbers from least to greatest. 7,11,15,15,16,18,19,20,21 After you do that you will find the numbers that are in the center and that will be your median.
$
6
4
No
2+
of
black
tan
gray white
Color
green
orange
O green
O orange
(a) Which color had the fewest T-shirts sold?
black
o tan
O gray O white
How many T-shirts of that color were sold?
T-shirt(s)
(b) How many more gray T-shirts were sold than tan T-shirts?
more T-shirt(s) sold
(C) For how many colors were there fewer than 10 T-shirts sold?
color(s)
Explanation
Check
© 2022 McGraw HIN
Answer:
a. tan
3 T-shirts
b. 7 - 3 = 4 T-shirts
For the polynomial f(X)=2x^3-9x^2+11x-20
As
X -> -♾️,f(X) -> ♾️
A. True
B. False
Answer:
False
Step-by-step explanation:
I'm assuming its because x isn't negative infinity because the leading coefficient is positive
6. Freddy gets an allowance of £50 each month.
His parents increase is by 35%. How much does
Freddy now receive for his allowance?
Answer:
$67.5
Step-by-step explanation:
New value =
50 + Percentage increase =
50 + (35% × 50) =
50 + 35% × 50 =
(1 + 35%) × 50 =
(100% + 35%) × 50 =
135% × 50 =
135 ÷ 100 × 50 =
135 × 50 ÷ 100 =
6,750 ÷ 100 =
67.5
20 characters just for you brainly
Answer:
first and last option
Step-by-step explanation:
the first and the last are increasing from left to right since the slope is positive.
Consider this graph of a standard normal curve.
What percentage of data is represented by the shaded area?
Enter your answer as a number, like this: 42%
|-108| divided by |36|+|17|
What is the equation
of the line that passes through the point (-2, -3) and has a
slope of -1?
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
given : m = -1
the equation is : y = -x+b
through the point (-2,-3) :-3 =-(-2)+b....... b=-5
the equation is : y = -x-5
absolute value of 19/24
Answer:
-19/-24 ?
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −19 and 0 is 19 .
-24 has an absolute value of 24
Answer:
0.791666667 I hope this helped
Step-by-step explanation:
A person who can afford a monthly payment of __________ and signed a mortgage with a monthly payment of __________ was most likely the victim of predatory lending.
A. $900; $1000
B. $900; $800
C. $900; $900
D. $900; $700
Answer:
A . 900-1000
Step-by-step explanation:
The first term of an A.P is 3 and the fifth term is 9.Find the number of terms in the progression if the sum of the progression is 81.
Answer:
its A becauss i tryed b and th en i tried A so its a
HURRY!!!!
What is the volume, in cubic inches, of the right rectangular prism with a length of 5 inches, a width of 8 inches, and a height of 20 inches?
