Answers
Answer:
Let
x=sin-¹u
Sinx=u
let y=tan-¹v
tany=v
Substituting
Sin[x + y]
Applying the sine expansion
Sinxcosy + CosxSiny
Recall x =Sin-¹u
y=tan-¹v
Sin(Sin-¹u)Cos(tan-¹v) +Cos(sin-¹u)Sin(tan-¹v)
Now at this point
Here's what you do
For the first expression
Sin(Sin-¹u)
Let's simplify this
Let P = Sin-¹u
Taking sine of both sides
SinP=u
Draw a Right angled angle for this
Since Sine from SOHCAHTOA is OPP/HYP
Where P is the angle and u is the opposite and 1 is the hypotenuse since u is the same as u/1
substituting Sin-¹u = P
You have
Sin(Sin-¹u) = SinP
and from the triangle you drew
SinP = u
Taking the second express
Cos(tan-¹v)
Let Q=Tan-¹v
taking tan of both sides
tanQ=v
Draw a right angled triangle for this too
Since Tan from SOHCAHTOA is OPP/ADJ
Find the Hypotenuse cos you'll need it
Now Let's do the substitution again
We first said tan-¹v = Q
When we substitute it in Cos(tan-¹v)
We have CosQ
Cos Q from the second right angle triangle you drew is 1/√1+v²
Because CAH is adj/Hyp
So
the first part of the original Express
Which is
Sin(Sin-¹u)Cos(tan-¹v) is now simplified to
u(1/√1+v²).
Let's Move to the second part of the Original Expression
Cos(Sin-¹u)Sin(tan-¹v)
From our first solution
We said Sin-¹u= P
So replacing it here
we have Cos(sin-¹u) = CosP
let's leave the second one for now which is sin(tan-1v) We'll deal with this after the first
so Cos(Sin-¹u) = CosP
we can still use our first Right angle triangle for this because the angle was P.
so Cos P from that triangle will be
CosP= √1-u²
Now onto the next
Sin(tan-¹v)
From the Second solution of the first we did
we said let Tan-¹v =Q
Substituting this
we have
Sin(tan-¹v) = SinQ
using the second Right angle triangle because its angle is Q
We have
SinQ= v/√1+v²
Answer for second phase Which is
Cos(sin-¹u)Sin(tan-¹v) = √1-u²(v/√1+v²)
We're done
compiling our answers
The answer to
Sin(Sin-¹u - tan-¹v) = u(1/√1+v²) + [(√1-u²)(v/√1+v²)]
You can still choose to factor out 1/√1+v² since it appears on both sides
Related Questions
The weatherman says that there is a 90% chance of rain tomorrow. Find the odds that it will rain tomorrow.
Answers
Answer:
9 out of 10
Step-by-step explanation:
90 percent chance simply means 90÷100
Which is 9 out of 10
what is y -5= 2/3(x-2) in slope intercept form??
Answers
Answer:
y = 2/3x + 3 2/3
Step-by-step explanation:
slope intercept form: y = mx + b
isolate the y => y = 2/3(x - 2) + 5 => y = 2/3x - 4/3 + 5 => y = 2/3x + 3 2/3
A skateboarding ramp is 17 in high and rises at an angle of 19"How long is the base of the ramp ? Round to nearest inch
Answers
Answer: 39.3 inches
Step-by-step explanation:
Let x represent the length of base of ramp.
We have been given that a skateboarding ramp is 12 in high and rises at an angle of 17 degrees. We are asked to find the base of the skateboard.
The height of ramp, the base of ramp and angle of elevation make a right triangle with ground, where, 12 inch is opposite side and base of ramp is adjacent side of angle of elevation.
Therefore, the base of ramp is 39.3 inches long.
What is 972 written in standard form
Answers
Answer:
we will write 972 in standard form
Step-by-step explanation:
Standard form of a given number 972 is equals to 9.72 × 10².
What is standard form?" Standard form is defined as the mathematical expression, number, any equation , quantity with certain rules defined for it."
According to the question,
Given number = 972
Standard form of writing a number is
Given number should be express as a decimal number between 1.0 to 10.0
multiply by power of 10.
Standard form of 972 = 9.72 × 10²
Hence , standard form of a given number 972 is equals to 9.72 × 10².
Learn more about standard form here
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A line passes through the point (-9,5) and has a slope of
4/3
Write an equation in point-slope form for this line.
Answers
Answer:
y=4x/3+17
Step-by-step explanation:
4/3=y-5/x+9
y=4x/3+17
The equation in point-slope form for this line is -
(y - 5) = (4/3)(x + 9)
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have a line that passes through the point (-9,5) and has a slope of
4/3.
The point slope form is given by -
(y - y₁) = m(x - x₁)
Now, we can write the equation as -
(y - 5) = (4/3)(x + 9)
Therefore, the equation in point-slope form for this line is -
(y - 5) = (4/3)(x + 9)
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Please help me A line that includes the point (3, 3) has a slope of 4. What
is its equation in slope-intercept form?
Answers
Answer:You can do this two ways: Either use the slope intercept form
y = mx + b with slope m=-2 so y = -2x +b
From that use x=5, y = -3 to solve for b
-3 = -2(5) + b
-3 = -10 + b
10-3 = b
7 = b
Your equation is: y = -2x + 7
OR
Use the point slope formula: y - y1 = m(x-x1)
with m = -2, (x1, y1) = (5,-3)
y-(-3) = -2(x-5)
y + 3 = -2x + 10
y = -2x + 10 - 3
y = -2x + 7
Step-by-step explanation:
please solve rhis ques
Answers
Answer:
The highest common factor is (a + b)
Step-by-step explanation:
We start by making a factorization of the first expression
By using the difference of two squares, we can have it as;
a^2 - b^2 = (a + b)(a-b)
For the second expression, we already have;
(a + b)^2 = (a + b)(a + b)
What this mean is that (a + b) is common to both expressions and we have it as the highest common factor
I NEED HELP PLEASE 10 point!!!!
Answers
Answer:
Step-by-step explanation:
2 root ( 5,0)
y intercept (0,5)
What percent of 21 is 105?
Answers
Answer:
20%
Step-by-step explanation:
21/ 105
= 0.2 x 100
20%
(21*100):105 =
2100:105 = 20
PLEASE SOLVE. FIRST ANSWER WITH EXPLANATION GETS MOST BRAINLIEST AND 10 POINTS. THANKS ;)
Answers
Thus, 360 = 2(2x + 10) + 2(x+ 5)
360 = 2(2x + 10 + x + 5)
360 = 2(3x + 15)
180 = 3x + 15
165 = 3x
x = 55
Lupe needs to make a poster that is 2 m by 4 m for the big game. The cost of the paper is $1.75. Later she needs another poster with dimensions 1 m by 2 m. What is the paper for this poster likely to cost
Answers
Answer:
$0.42
Step-by-step explanation:
Given data
Dimension
Length=4m
Width=2m
Cost= $1.75
Area= 4*2= 8m^2
Cost per area=1.75/8
Cost per area=$0.21 per m^2
The new poster's dimension
Lenght =2m
Width= 1m
Area= 2*1= 2m^2
Hence if a square meter cost $0.21
Then 2 square meter will cost x
cross multiply
2*0.21=x
x=$0.42
Hence the new poster will cost $0.42
find the value of x plsss helpp
Answers
Answer:
90 + 29 + x = 180
119 + x = 180
-119 -119
X = 61 degrees
A triangle will always equal 180 degrees.
Given that there is a right triangle it is 90 degrees, also given that 29 degrees is there we add those and add x (the unknown degree) to equal 180 degrees.
PLEASE HELP ME! THIS IS DUE TODAY, AND I WILL MARK BRAINLEST.
Answers
Answer:
The correct answer is B: XY=4 cm
Step-by-step explanation:
This is correct because the triangles are both leaning in the same direction so the sides are congruent as stated. Congruent, means that they are equal to each other in other words symmetrical. Because of this, they are the same triangle so where 4 is on the first triangle, it will appear on the same side on the other triangle. This means the answer is B. XY = 4 cm
Answer:
The second one
Step-by-step explanation:
It cant be the first because YZ=4cm
cant be the third because m∠Y= 50°
cant be the forth one because m∠Z= 70°
so, it has to be the second one because XY≅AB
so, if AB=4cm then XY=4cm
Hello i really need help i got 1/36 but I wanna be sure thanks
Answers
Answer:
You are correct great job! I believe you did
1/4 × 1/9 = 1/36 If so thats exactly the right method!
Please help besties!
Answers
Which are examples of non-statistical questions?
Questions
Question 1 What is Sasha’s favorite movie?
Question 2 What is Stacey’s favorite book?
Question 3 What is your favorite movie?
Question 4 What is your favorite book?
questions 1 and 2
questions 1 and 3
questions 2 and 4
questions 2 and 3
Answers
Answer:
A 1 and 2
Step-by-step explanation:
SA = 2pi * r ^ 2 + 2pi * r * h (Use 3.14 for .) How much metal is needed to create a trash can with a height of 4 feet and a base radius of 1 foot? (Find the surface area of the cylinder.) pi square feet Do NOT round your answer.
Answers
Answer:123
Step-by-step explanation:
Rebecca paid $16.90 to place an advertisement in a local
newspaper. The newspaper charged $4.50 set up fee and $0.40
per word. How many words were in Rebecca's advertisement?
Answers
12.40/0.4 = 31 words in the ad
Answer:
31 words
Step-by-step explanation:
because the set up fee is 4:50$, minus this from the price Rebecca payed
16.90-4.50=$12.40
now divide this amount by $0.40 in order to get her word count
12.40÷0.40=31
find the value of X and Y triangle BLT is congruent to Triangle JFK
Answers
Using the order of the letters in the triangles find the corresponding sides:
BL is similar to JF
LT is similar to KF
BT is similar to JK
Find the scale between LT and KF
9/12 = 3/4
The smaller triangle is 3/4 the size of the lager one.
This means BT = 3/4(JK) = 3/4(4) = 3
So x = 3, so side BL = 2x = 2(3) = 6
Now to solve for y:
BL is 3/4(JF)
6 = 3/4(y)
Solve for y by dividing both sides by 3/4
Y = 6/(3/4)
Y = 8
X = 3, y = 8
A pendulum is constructed by attaching a 4m rope to a bowling ball. It is then displaced 2m to one side and released.
Ignoring all effects of friction, and without knots,
a) Determine the period of the pendulum. Round to one decimal place.
Answers
Answer:
T = 4.0 s
Step-by-step explanation:
The period of a simple pendulum is given by
[tex]period = 2\pi \sqrt{ \frac{l}{g} } [/tex]
where l = length of the pendulum
= 4 m
g = acceleration due to gravity
= 9.8 m/s^2
[tex]period = 2\pi \sqrt{ \frac{(4 \: m)}{(9.8 \: \frac{m}{ {s}^{2} } )} } = 4.0 \: s[/tex]
Find a pair of complementary angles. Show work to prove they are complementary.
Answers
Answer:
Hello! answer: 45 and 45 is a complementary angle and 60 and 30 is a complementary angle
Step-by-step explanation:
Complementary angles are just angles that add up to 90 degrees so... 45 + 45 = 90 60 + 30 = 90 so that is how those are complementary angles.
Hope that helps!
Answer:
angle QRT/angle VRT and angle SRW/angle WRV
Step-by-step explanation:
QRT and VRT: Both angles are 45 degrees, adding those degrees together gets you 90 degree angles meaning that they are complementary.
SRW and WRV: 60 plus 30 is equal to 90 making them complementary angles as right angles are 90 degrees
HELP ME PLEASE!!! I’ll mark brainly
Answers
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
yes
7th Grade triangle measurements
Answers
Answer:
ummmmmm....post the pic at least
Can someone please help me in this question
Answers
Step-by-step explanation:
a) Let y = f(x) = 3x - 2x^2
f(-2) = 3(-2) - 2(-2)^2 = p
= -6 - 8
= -14
= p
f(2.5) = 3(2.5) - 2(2.5)^2 = q
= 7.5 - 12.5
= -5
= q
b) graphing
c) From the graph, you should be able to verify the following:
i) f(0.5) = 3(0.5) - 2(0.5)^2 = 1
ii) 0.5 = 3x - 2x^2 or x = 1.3, 0.2
iii) the maximum occurs at
f(0.75) = 1.125
d) the equation for the line of symmetry is x = 0.75
3/2 ( x - 6 ) = -3
What's x?
A. x = -8
B. x = 2
C. x = 4
D. x = 9
Answers
Answer:
The answer is C.
Step-by-step explanation:
Had this on a quiz.
What is true about this cylinder?
Answers
Answer:
2
Step-by-step explanation:
.....................
PLEASE ANSWER QUICKLY
Answers
Answer: 17
Step-by-step explanation:
Answer:
B) 17
Step-by-step explanation:
Prime numbers are numbers that are not products of two smaller natural numbers. Everything except 17 is not prime cuz they can be derived from multiplying other numbers but 17 cannot be.
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter. To the nearest inch, how many inches are in 2 meters?
Answers
Answer:
1400 cm/ 2.54 cm per inch = 551 inches. Step-by-step explanation: There are 39.3701 inches in 1 meter, so all you have to do is multiply. :) 551 inches.Step-by-step explanation:
The slideat the playground has a height of 6ft. The base of the slide measured on the ground is 8ft. What is the length of the slide?
Answers
Answer:
10 ft
Step-by-step explanation:
The length of the slide can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
6² + 8² =
36 + 64 = 100
c = √100
c = 10
Distance between -12 and
12
Answers
Answer:
24
Step-by-step explanation:
Explanation: from -12 to 12 you count up from -12 back to zero then up to 12. So all in all you move 24 to get from -12 to 12.