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]
There were 425 people at a cinema when the movie started. One hour later, there were 323 people left at the cinema. What was the percentage decrease in the number of people at the cinema
Answer:
83% Might be wrong
Step-by-step explanation:
Answer:
24% Positive.
x=7
Step-by-step explanation:
0.
A mountain climber ascends a mountain to its peak. The peak is 14,090 ft above sea level. The climber then descends 490 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.
13,600 ft
14,580 ft
–13,600 ft
9,190 ft
Answer:
13,600 feet above sea level
Step-by-step explanation:
The climber was at 14,090 feet above sea level, and then they went 490 feet closer to sea level to meet the other climber. Since they’re moving closer to sea level and you want to know how far *above* sea level they are, subtract 490 from 14,090. 14,090-490=13,600 feet above sea level
1:
What is the area of the right triangle in this coordinate plane?
2
3
5
6
8
9
A
Write the equation for the line L shown in the figure
the coordinate is (2, -2).
17. Which of the following is an equivalent expression
to x2 + 6x + 112
A. (x - 3)²+3
B. (x + 3)2 + 2
C. (x + 2)2 + 3
D. (x – 3)2 + 2
Answer:
A={x-3}^2 +3Step-by-step explanation:
(x+3) (x+3)+3
x(x+3)+3(x+3)+3
x2+3x+3x+9+3
x2+6x+12
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
Find the circumference and the area of a circle with diameter 9cm. Use the value 3.14 for pie and do not round your answer. Be sure to include the correct units in your answer
Answer:
Circumference = 28.26
Area = 63.585 cm²
Step-by-step explanation:
Formula for Circumference:
C = 2 × π × r
C = Circumference
r = radius
Radius = Diameter ÷ 2
9 ÷ 2 = 4.5
C = 2(3.14)(4.5)
C = 28.26
Formula for Area:
A = π × r²
9 ÷ 2 = 4.5
4.5 is the radius.
A = (3.14)(4.5)²
Simplify:
(3.14)(20.25)
= 63.585 cm²
6. Claim: = 0.01.
Population statistics: = 52 and = 68
Sample statistics:
5595, N1
156 and X2 = 5575, n2 = 216
Answer:
false
Step-by-step explanation:
you have to multiply the 52 and 68, making the n1 = 5577, not 5575
What would be the best estimate for the height of a front door?
Answer: The height of a standard door is about 2 m. The length of an adult pace is about 1 m. The length of a size 8 shoe is about 30 cm. Most adults are between 1.5 m and 1.8 m in height.
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
response will be saved automatically.
Three students performed a science experiment using sugar and a beaker.
The beaker contained 570.3 grams of sugar before the experiment
started. During the experiment, each of the 3 students removed 42.34
grams of sugar from the beaker.
How much sugar, in grams, was left in the beaker at the end of the
experiment?
Show your work.
Answer
grams
B
T>
x
Answer:
443.28
Step-by-step explanation:
Subtract 42.24 from 570.3 three times.
(b) Work out an equation of the straight line that passes through (9, 2) and (3,5)
[3 marks]
Answer:
I think it's y = -x + 11
Step-by-step explanation:
use the formula y - y1/ y2 - y1 = x - x1/ x2 - x1
What is the volume of the pyramid?
*Do NOT round your answer!
Answer:
V ≈ 611
Step-by-step explanation:
Solution
V = l w h ÷ 3 = 14.1 × 13 × 10 / 3 ≈ 611
Jada was measuring the dimensions of her new closet. The area of the closet is 8 1/6 square feet and the width of the closet is 3 1/2 What is the length of her closet?
Answer: 2 1/3 feet
Step-by-step explanation:
Area of closet = 8 1/6 feet ²
Width of the closet = 3 1/2 feet
Length of the closet = Unknown
We should note that:
Area = Length × Width
Length = Area / Width
Length = 8 1/6 ÷ 3 1/2
= 49/6 ÷ 7/2
= 49/6 × 2/7
= 7/3
= 2 1/3 feet
The length is 2 1/3 feet
8.3 is equal to -----------hundredths
Answer:
830
Step-by-step explanation:
Answer: it would be 83 hundredths
Step-by-step explanation:
8.3x10 = 83
Can someone help me figure out how to do this?
Stuck trying to solve this, didn’t pay attention :/
Answer:
Pay attention next time
1x+2y=5 find four solutions
Answer:
Simplifying
1x + 2y = 5
Solving
1x + 2y = 5
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2y' to each side of the equation.
1x + 2y + -2y = 5 + -2y
Combine like terms: 2y + -2y = 0
1x + 0 = 5 + -2y
1x = 5 + -2y
Divide each side by '1'.
x = 5 + -2y
Simplifying
x = 5 + -2y
Step-by-step explanation:
Find the missing side length.
Answer:
[tex]a = 4 \\ b = 2 \sqrt{2} [/tex]
Its a right angle triangle so trigonometry is used.
a is the hypotenuse, b is the adjacent.
Use sin to find a. Use tan to find b.
HELP PLEASE IM BEING TIMED
Answer:g
Step-by-step explanation: because those sides equal one another if you flip them them same way
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 :)
need help ASAP!!! anyone know ??????
Answer:
D
Step-by-step explanation:
Calculate and express your answer in decimal form. 12⋅17
Answer:
12·17=207 But if you need it in a decimal, I'd say 2.07. Hope this helps!! (:
Write the inequality represented by each graph..
Graph one : (0,-1) (6,3)
Graph two : (0,3) (4,-5)
Help
Answer:
Step-by-step explanation:
HERE ARE THE ANSWERS
What is 8 x 3? I'm doing an i-ready lesson and I forgot, please help me XD
Answer: 24
Step-by-step explanation:
Solve for 2.
=
E
2
3
А
9
B
6
D
Answer:
9/3 = 15/x
45 = 9x
x=5
Let me know if this helps!
Which best explains whether or not all isosceles triangles are similar?
All isosceles triangles are similar. Two angles within each triangle are always congruent.
All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.
All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.
Answer:
C: All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
Step-by-step explanation:
An Isosceles triangle is one that 2 of it's sides are equal and thus two of its angles are congruent which means they are equal.
Now, another Isosceles triangle may not necessarily be similar to another one because the congruent angles in one Isosceles triangle may not be the same with that of another Isosceles triangle.
Thus, correct answer is option C
Answer:
C, I think I hope you all do well on your test!!!!
Step-by-step explanation:
(Asapppppp!!)
Simplify to create an equivalent expression,
19 - 6(-k - 2)
Choose 1 answer,
A.-6k+31
B.25k+7
C.6k+31
D.25k+32
Answer:
56/1230
Step-by-step explanation:
Help me or pretty please
Answer:
The unknown information is how many months she will use her phone, and how many GB she will download. We can represent these with literally any non-number symbol, letters, greek letters (if ur cool), but to simplify it we can represent the number of months with 'm' and the number gigabytes with 'g'
21m + 3g ≤ 30
Step-by-step explanation: