i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.
Answer:
[tex]sin\ \varnothing = \frac{-1}{10}\sqrt 2[/tex]
[tex]cos\ \varnothing = \frac{-7}{10}\sqrt 2[/tex]
[tex]tan\ \varnothing = \frac{1}{7}[/tex]
[tex]cot\ \varnothing = 7[/tex]
[tex]sec\ \varnothing = \frac{-5}{7}\sqrt 2[/tex]
[tex]csc\ \varnothing = -5\sqrt 2[/tex]
Step-by-step explanation:
Given
[tex]N = (-7,-1)[/tex] --- terminal side of [tex]\varnothing[/tex]
Required
Determine the values of trigonometric functions of [tex]\varnothing[/tex].
For [tex]\varnothing[/tex], the trigonometry ratios are:
[tex]sin\ \varnothing = \frac{y}{r}[/tex] [tex]cos\ \varnothing = \frac{x}{r}[/tex] [tex]tan\ \varnothing = \frac{y}{x}[/tex]
[tex]cot\ \varnothing = \frac{x}{y}[/tex] [tex]sec\ \varnothing = \frac{r}{x}[/tex] [tex]csc\ \varnothing = \frac{r}{y}[/tex]
Where:
[tex]r^2 = x^2 + y^2[/tex]
[tex]r = \sqrt{x^2 + y^2[/tex]
In [tex]N = (-7,-1)[/tex]
[tex]x = -7[/tex] and [tex]y = -1[/tex]
So:
[tex]r = \sqrt{(-7)^2 + (-1)^2[/tex]
[tex]r = \sqrt{50[/tex]
[tex]r = \sqrt{25 * 2[/tex]
[tex]r = \sqrt{25} * \sqrt 2[/tex]
[tex]r = 5 * \sqrt 2[/tex]
[tex]r = 5 \sqrt 2[/tex]
Solving the trigonometry functions
[tex]sin\ \varnothing = \frac{y}{r}[/tex]
[tex]sin\ \varnothing = \frac{-1}{5\sqrt 2}[/tex]
Rationalize:
[tex]sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]sin\ \varnothing = \frac{-\sqrt 2}{5*2}[/tex]
[tex]sin\ \varnothing = \frac{-\sqrt 2}{10}[/tex]
[tex]sin\ \varnothing = \frac{-1}{10}\sqrt 2[/tex]
[tex]cos\ \varnothing = \frac{x}{r}[/tex]
[tex]cos\ \varnothing = \frac{-7}{5\sqrt 2}[/tex]
Rationalize
[tex]cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}[/tex]
[tex]cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}[/tex]
[tex]cos\ \varnothing = \frac{-7\sqrt 2}{10}[/tex]
[tex]cos\ \varnothing = \frac{-7}{10}\sqrt 2[/tex]
[tex]tan\ \varnothing = \frac{y}{x}[/tex]
[tex]tan\ \varnothing = \frac{-1}{-7}[/tex]
[tex]tan\ \varnothing = \frac{1}{7}[/tex]
[tex]cot\ \varnothing = \frac{x}{y}[/tex]
[tex]cot\ \varnothing = \frac{-7}{-1}[/tex]
[tex]cot\ \varnothing = 7[/tex]
[tex]sec\ \varnothing = \frac{r}{x}[/tex]
[tex]sec\ \varnothing = \frac{5\sqrt 2}{-7}[/tex]
[tex]sec\ \varnothing = \frac{-5}{7}\sqrt 2[/tex]
[tex]csc\ \varnothing = \frac{r}{y}[/tex]
[tex]csc\ \varnothing = \frac{5\sqrt 2}{-1}[/tex]
[tex]csc\ \varnothing = -5\sqrt 2[/tex]
Find the volume of the cone-
Answer:
12.6ft³
Step-by-step explanation:
Hey There!
So the first thing we need to do is find the formula for volume of a cone
[tex]V=\pi r^{2} \frac{h}{3}[/tex]
r = radius
h = hypotenuse
Now all we have to do is plug in the hypotenuse and the radius
[tex]V=\pi 2^{2} \frac{3}{3}[/tex]
2²=4
[tex]\frac{3}{3} =1[/tex]
4xπ=12.5663706144
And now we just round to the nearest tenth
so we can conclude that the volume of the cone is 12.6ft³
need help ASAP!!! anyone know ??????
Answer:
D
Step-by-step explanation:
Will mark b for right answer !!!!!
( calculate angels using line and angle relationships)
Answer:
56
Step-by-step explanation:
because it is a right angle so 90 _ 34 = 56
Answer:
the answer should be 56 as 90-34=56
Is (3, 3) a solution to the equation y
=
x?
yes
no
Answer:
yes
Step-by-step explanation:
HELP DUE AT MIDNIGHT
Answer:
Will you give brainliest? I know the answer. Only if you would give brainliest.
Step-by-step explanation:
Are triangles congruent if three pairs of corresponding sides are
congruent? Pls help me.
Answer:
if triangles are congruent if three pairs of corresponding sides are
congruent.to made a congruent triangle
following axiom need to fulfilled.
A.S.A AXIOMS.S.S. AXIOMS.A.S. AXIOMAnswer:
to my knowledge yes they are
Step-by-step explanation:
A farmer is creating a budget for planting soybeans and wheat. Planting soybeans costs $200 per acre and planting wheat costs $500 per acre. He wants to spend no more than $100,000 planting soybeans and wheat. What is the "multiplier" for soybeans?
Answer:
5 acres < soybeans < 495
2 acres < wheat < 198 acres
Step-by-step explanation:
If farmer plans to plant minimum of soybeans, it should be 5 acres of soybeans costing $1000. The remaining cost of $98,000 will be available for maximum of wheat, i.e., 198 acres of wheat.
Similarly, if we go for minimum possible planting for wheat, it should be 2 acres, and then resulting in 495 acres for soybeans
5 acres < soyabeans < 495
2 acres < wheat < 198 acres
Answer:
The multiplier for soybeans is 200, which is dollars per acre.
Step-by-step explanation:
5 acres ≤ soybeans ≤ 495 acres (constraint)
2 acres ≤ wheat ≤ 198 acres (constraint)
150w + 125s = 100,000
This would represent 150 acres of wheat and 125 acres of soybeans. The acres of wheat would add up to $75,000 because 150 x 500 = 75,000 and the acres of soybeans would add up to $25,000 because 125 x 200 = 25,000. (example of a solution, there are more possible)
A right rectangular prism has a square base and a volume of 225 cubic centimeters. The height, h, of the prism is 9 centimeters. Find the area of the base, B. A. B. C. D.
Answer:
Area of base = 25cm
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
Volume = length × width × height = lwh
for a square base, length = width
∴ volume = l × l × h = l²h
where:
l = length
h = height = 9cm
volume = 225 cm³
∴ 225 = l² × 9
l² = 225 ÷ 9
l² = 25
∴ length = √ 25 = 5cm
Area of base = Length × Length = 5 × 5 = 25cm
A quartic polynomial P(x) has rational coefficients. If 2 − i and-√5 are roots of P(x) = 0, what are the other 2 roots?
Answer:
2 + i and + √5
Step-by-step explanation:
Since P(x) is a quartic equation, it has 4 roots.
Since 2 - i and -√5 are two of its roots, then its conjugate pairs of 2 + i and + √5 are its other two roots.
So, its other two roots are 2 + i and + √5
WILL REWARD BRAINLIEST (40 POINTS PLEASE HELP)
Answer:
first of all I can't see nothing
x2 - 18x + 81
True or False?
Your FACTOR is when you SQUARE your B value.
in this way you can solve this
I need help with this answer I would like help !
If a plane traveled 610 miles in 1 hour, how fast is it going?
Answer:
very fast
Step-by-step explanation:
10.2 miles per minute :)
Please help me out! And please show your work!
What is meant by the order of operations?
Answer:
Step-by-step explanation: The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Choose Yes or No to tell whether the Addition Property of Inequality can be used to solve each statement.
1. w – 4 > –10
2. 12 ≥ 20x
3. 7y10 ≤ 5.5
4. –3.25 < x – 9.75
Answer:
yes,no, no, yes
Step-by-step explanation:
25% of what number is 20
Answer:
100
Step-by-step explanation:
whats12 divided by 1/3 (infractions)
12 divided by 1/3 is also equal to 12 times 3.
12x3=36
To double check, you could use a calculator, but the answer would still be 36.
sorry if this doesn't help
Answer:
36/1
36
Step-by-step explanation:
A scenery is painted on a paper 44cm long and 30cm wide such that there is a margin of 2cm along each of its sides. Find the total area of the margin.
Answer:
280 cm²
Step-by-step explanation:
The computation of the total area of the margin is shown below:
Given that
Length = 44 cm
Breadth = 30 cm
Area of the cardboard = 44 × 30 cm² = 1,320 cm²
Now
Length of the painting eliminating the margin is
= [44 - (2 + 2)] cm
= 40 cm
And,
Breadth of the painting eliminating the margin is
= 30 - (2+ 2)
= 26 cm
Now
Area of the painting eliminating the margin is
= (40 × 26) cm²
= 1,040 cm²
And, finally the total area of the margin is
= (1,320 - 1,040) cm²
= 280 cm²
Which inequality represents all possible solutions of - 4n<16?
4n is the soultioncAnswer:
Step-by-step explanation:
what is the relative frequency as a percent to the nearest tenths of males and females who ride their bike to school when compared to the total population?
Answer:
100 percent - 18 percent
Step-by-step explanation:
answer will come
0.6x + 2.7 = 0.9x
"solve the equation. show all your steps"
Answer:
x=9
Step-by-step explanation:
0.6x+2.7=0.9x
move the terms
0.6x-0.9x=-2.7
collect like terms
-0.3x=-2.7
divide both sides
x=9
Jordan runs 20% of a marathon relay race. If a
marathon course is 25 miles long, how many miles
does Jordan run?
I’m
Answer:
5
Step-by-step explanation:
Answer:
5 miles
Step-by-step explanation:
Take 20% of 25, you can do this by multiplying the decimal form of 20% by 25:
0.20 x 25 = 5
HELP PLEASE IM BEING TIMED
Answer:g
Step-by-step explanation: because those sides equal one another if you flip them them same way
what's the percentage of change from 20 is decreased to 11
Answer:
The percentage is 45 percent.
Step-by-step explanation:
If your scale factor is 3/4, how will the scaled copy compare to the original?
It will be the same size.
It will be larger.
It will be smaller.
A square has a radius of 10 ft. Find the area of the square
Answer:
Hello hello
Step-by-step explanation:
Answer:
a square does not have a radius
Step-by-step explanation:
but you can find the area by squaring one side
I need help on both
A company was able to incite staff from 100 employees to 214 employees. What was the percentage increase in staff
Answer:
114%
Step-by-step explanation:
A company was able to incite staff from 100 employees to 214 employees. What was the percentage increase in staff?
Percentage Formula is given as:
New value - Old value/Old value × 100%
New value = 214
Old value = 100
Hence:
Percentage increase = 214 - 100/100 × 100
= 114/100 × 100
= 114 %
Therefore, the percentage increase = 114%