Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator. -135^{\circ}−135
Answers
Answer:
Step-by-step explanation:
Let's take a look at the given angle 135°
The sketch of the angle which corresponds to [tex]-\dfrac{3\pi}{4}[/tex] unit circle and can be seen in the attached image below;
The trigonometric ratios are as follows for an angle θ on the unit circle:
Trigonometric ratio related ratio on coordinate axes
sin θ [tex]\dfrac{y}{1}[/tex]
cos θ [tex]\dfrac{x}{1}[/tex]
tan θ [tex]\dfrac{y}{x}[/tex]
csc θ [tex]\dfrac{1}{y}[/tex]
sec θ [tex]\dfrac{1}{x}[/tex]
cot θ [tex]\dfrac{x}{y}[/tex]
From the sketch of the image attached below;
The six trigonometric ratio for 135° can be expressed as follows:
[tex]sin (-\dfrac{3\pi}{4})= \dfrac{y}{1}[/tex]
[tex]sin (-\dfrac{3\pi}{4})=- \dfrac{\sqrt{2}}{2}[/tex]
[tex]cos (-\dfrac{3\pi}{4})= \dfrac{x}{1}[/tex]
[tex]cos (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= \dfrac{y}{x}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= \dfrac{-\dfrac{\sqrt{2}}{2}}{-\dfrac{\sqrt{2}}{2}}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}} \times {-\dfrac{2}{\sqrt{2}}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= 1[/tex]
[tex]csc (-\dfrac{3\pi}{4})= \dfrac{1}{y} \\ \\ csc (-\dfrac{3\pi}{4})=\dfrac{1}{-\dfrac{\sqrt{2}}{2}} \\ \\ csc=1 \times -\dfrac{2}{\sqrt{2}} \\ \\csc =-\sqrt{2}[/tex]
[tex]sec (-\dfrac{3 \pi}{4})=\dfrac{1}{x} \\ \\ sec = \dfrac{1}{(-\dfrac{\sqrt{2}}{2})} \\ \\ sec = 1 \times -\dfrac{2}{\sqrt{2}} \\ \\ sec = - \sqrt{2}[/tex]
[tex]cot(-\dfrac{3 \pi}{4}) = \dfrac{x}{y} \\ \\ cot(-\dfrac{3 \pi}{4}) = \dfrac{-\dfrac{\sqrt{2}}{2} }{-\dfrac{\sqrt{2}}{2}} \\ \\ cot(-\dfrac{3 \pi}{4})= -\dfrac{\sqrt{2}}{2} } \times {-\dfrac{2}{\sqrt{2}}} \\ \\ cot (-\dfrac{3 \pi}{4}) = 1[/tex]
Related Questions
PLEASE help i neeed help asap im willing to give u 100 or 40 points if u answer this correctly so please help answer them all
what is 50.30 rounded to the nearest hundredth?
what is 50.20 rounded to the nearest hundredth?
what is 56.90 rounded to the nearest hundredth?
what is 49.50 rounded to the nearest hundredth?
what is 51.10 rounded to the nearest hundredth?
what is 30.00 rounded to the nearest hundredth?
Answers
Step-by-step explanation:
The hundredth place is the second number to the right of the decimal place (e.g., in ab.cd, where a, b, c, and d represent digits, the hundredth place is d).
When we round to the nearest hundredth, we remove all digits after the thousandth place. Then, if the thousandth place is 5 or greater, we remove it and add 0.01 (round up); if the thousandth place is 4 or lesser, we remove it (round down).
Thus:
50.30=50.30, as there is no thousandth place
50.20=50.20, same reasoning
56.90=56.90, same reasoning
49.50=49.50, same reasoning
51.10=51.10, same reasoning
30.00=30.00, same reasoning
Given that the measure of ∠x is 149°, and the measure of ∠y is 110°, find the measure of ∠z.
Answers
Answer:
∠z is 79°
Step-by-step explanation:
If your employer pays for 68% of your premium what percent do you have
to pay? *
32%
83%
42%
100%
Answers
Answer:
32%
Step-by-step explanation:
The employer has paid 68% of you premium, so there is 100%-68% = 32% remaining
add the fractions and simplify the 21/4 + 55/6 + 32/3
Answers
21/4+55/6=173/12 : 14 5/12
14 5/12 + 32/3 = 301/12 : 12 1/2
So the answer would be
12 and one half
Can someone help me please like fast ?
Answers
B. For the 2nd
-4,3. For the 3rd
C. The 4th
<. The 5th
>. And the 6th
What is i86?
-i
-1
i
1
Answers
B. -i
I'm not sure abt it but that's the answer that showed up hope that helps
Answer:
-1
Step-by-step explanation:
Which term of series1 +4+7+10+...is43
Answers
Answer:
a = 4
d = a2 - a1
d = 7 - 4
d = 3
an = 43
an = a + (n - 1)d
43 = 4 + (n - 1) 3
43 = 4 + 3n - 3
43 = 1 + 3n
43 - 1 = 3n
3n = 42
n = 42 ÷
n = 14
So, 14th term is 43
Please MARK AS BRAINLIEST
A triangular prism has a Volume of 375 cubic units. Find its Volume if all of
its dimensions were reduced to one-fifth their original length?
V=
cubic units.
Answers
10$ minus 1.25$ minus 3.18$
Answers
Answer:
Hello! answer: $5.57
Step-by-step explanation:
10.00 - 1.25 = 8.75
8.75 - 3.18 = 5.57
Hope that helps
Answer and Step-by-step explanation:
10 dollars - 1.25 dollars - 3.18 dollars =
$8.75 - $3.18 = $5.57
#teamtrees #PAW (Plant And Water)
Find the absolute value of -3.
Answers
Answer:
3
Step-by-step explanation:
If there is a negative sign in front of a number when trying to find absolute value, remove the negative sign. This is vice-versa if there is no negative sign. Have a Great Day and Hope this Helps :)
Answer: 3
Step-by-step explanation:
-3 is 3 spots away from the origin (0) when looking on a number line, and the absolute value is always the same number given(as a positive), even when it is negative
Example $4
A school sells adult play tickets for $7 and student tickets for the play for $4. If the school sold
420 student tickets, how many adult tickets were sold if the total sales for the play were $3010.
Answers
Answer:
190 adult tickets.
Step-by-step explanation:
Well,
420 × 4 = 1,680
3,010 - 1,680 = 1330
1330 ÷ 7 = 190.
So 190 adult tickets to the play were sold.
You're welcome,
Wolfie
helpppp:((( 10points!!!
14.) Loretta had a pitcher with 165 fl oz of
lemonade to pour into cups at the
birthday party. She filled each cup with
8 fl oz of lemonade until there was not
enough lemonade to completely fill
another cup. How many fluid ounces of
lemonade were left in the pitcher?
F.20 fluid ounces G.5fluid ounces H.21fluid ounces J.157fluid ounces
Answers
Answer:
20 fluid ounces
Step-by-step explanation:
165/8
Answer:
J.157 fluid ounces
Step-by-step explanation:
correct me if I'm wrong
Which number is less than 0.46?
Answers
Answer:
0.45 or 1/5 or 1/6
hope this helps
have a good day :)
Step-by-step explanation:
help meeeeeee pleassseeeeeee
Answers
Answer: triangular prism
Step-by-step explanation:
How do I find the right answer for b)
I got $2760.38 but the answer is $2760.37
Answers
Answer:
I guess u must not round it off
Step-by-step explanation:
in the bag, there are certain number of toy- blocks with alphabets A,B,C and D written on them. The ratio of blocks A:B:C:D is 4:7:3:1. if the number of A blocks is 50 more than the number of C blocks, what is the number of B blocks?
Answers
Let us consider the common ratio to be ‘x’.
So, toy blocks with alphabet A is 4x and
toy blocks with alphabet B is 7x and
toy blocks with alphabet C is 3x and
toy blocks with alphabet D is x
Again, the number of ‘A’ blocks is 50 more than the number of ‘C’ blocks.
As no. of ‘A’ and ‘C’ blocks are 4x and 3x respectively.
So,
4x=50 + 3x
x=50
Thus, the number of ‘B’ blocks is 7x = 7(50) = 350
350 is the required number.
9514 1404 393
Answer:
350
Step-by-step explanation:
There are 4 ratio units of A blocks and 3 ratio units of C blocks, so 1 more ratio unit of A blocks than of C blocks. That 1 ratio unit corresponds to 50 blocks, since there are 50 more A blocks than C blocks.
There are 7 ratio units of B blocks, so the number of B blocks is ...
7×(50 blocks) = 350 blocks . . . . . number of B blocks
Question #10 Evaluate the expression: 18-3(1+4)
Answers
Answer:
18-3-12
15-12
3 is the answer
hope this helps
have a good day :)
Step-by-step explanation:
Step-by-step explanation:
18-3(1+4)
multiply the numbers in the bracket by -3
18-3-12
3
Use a graphing tool to solve the equation below for x.
-3(-x) − 6 = -3x + 10
A. x ≈ -2.50
B. x ≈ 2.50
C. x ≈ -6.00
D. x ≈ -0.50
Answers
Answer:
C.
x ≈ 2.50
Step-by-step explanation:
The value of x in the given equation [tex]-3(-x) -6 = -3x+ 10[/tex] is 2.66
What is a line graph?A line graph is a type of chart used to show information that changes over time. We plot line graphs using several points connected by straight lines. We also call it a line chart. The line graph comprises of two axes known as 'x' axis and 'y' axis. The horizontal axis is known as the x-axis.
According to the given question.
We have a equation
[tex]-3(-x)-6 = -3x +10[/tex]
To draw a graph for the above equation we have to simplify the given equation.
Therefore,
[tex]-3(-x) -6 = -3x + 10[/tex]
⇒ [tex]+3x-6 = -3x + 10[/tex]
⇒[tex]3x+3x = 10 + 6[/tex]
⇒ [tex]6x = 16[/tex]
⇒ [tex]x = \frac{16}{6}[/tex]
⇒ [tex]x = 2.66[/tex]
After solving the above equation for x we have,
x = 2.66
⇒ A line which is parallel to y axis.
Therefore, we draw a line graph at a point x = 2.66 which is parallel to y axis.
Find out more information about line graph here:
https://brainly.com/question/23680294
#SPJ3
I really need help with this I don’t know where to start :(
Answers
Answer: answer is -4 5/12
Step-by-step explanation:
Answer:
-4 - 5/12, or option 3.
Step-by-step explanation:
Change the denominator of each fraction to a common denominator. In this situation, the common denominator between the three fractions is 12.
- 7 2/3 = - 7 8/12
- 5 1/2 = - 5 6/12
8 3/4 = 8 9/12
Add them together.
-7 8/12 - 5 6/12 + 8 9/12 =
First, add the whole numbers together.
-7 - 5 + 8 - 8/12 - 6/12 + 9/12 =
-12 + 8 - 8/12 - 6/12 + 9/12 =
-4 - 8/12 - 6/12 + 9/12 =
Now, add the numerators of the fractions together.
-4 + (-8 -6 + 9)/12
-4 + (-5)/12 =
-4 - 5/12
The answer is -4 - 5/12, or option 3.
A bank loaned out $15,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%?
How much of the $15,000 did the bank loan out at 7%?
Answers
9514 1404 393
Answer:
$5,500
Step-by-step explanation:
Let x represent the quantity loaned at 7%. Then the amount loaned at 17% is (15000-x), and the total interest is ...
0.07x +0.17(15000 -x) = 2000
-0.10x = -550 . . . . . . . . . collect terms, subtract 2550
x = -550/-0.10 = 5500 . . . . divide by the coefficient of x
The bank loaned $5,500 at 7%.
Lisa is a single taxpayer whose total income before deductions are $57,392. She was able to reduce her total income by $9,347 by filing Schedule A. Use the tax rate schedule below. How much did she save using Schedule A?
Answers
Answer:
$5554.91
Step-by-step explanation:
Which three steps are correct when solving this quadratic equation by completing the square?
x2 + 8x + 15 = 0
A)
x4 + 8x = -15
B)
x2 + 8x + 16 - 1
(x + 4)2 = 16
D)
(x + 4)2 = 1
E
x = -3 or x = 5
Answers
Answer:
E
Step-by-step explanation:
transferring the constant
making the coefficient of x^2 to be 1
then add the square of half the coefficient of x
take the square root of both sides
Round to the nearest tenth if necessary.
Find the distance between the two points.
(–1, –8), (–4, –4)
A)5
B)25
C)13
D)1
pls help will give brainliest.
Answers
Answer:
B) 25
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (-1, -8)
Point (-4, -4)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(-4--1)^2+(-4--8)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{(-3)^2+(4)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{9+16}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{25}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 5[/tex]4x + 3 < 9 someone please explain
Answers
Answer:
4x + 3 < 9
4x < 9-3
4x/4 <6/4
x=3/2
What is 72% of 83?
115.3
59.8
190
5100
Answers
Answer:
59.8
Step-by-step explanation:
Need help fast will give brainiest
Answers
Answers:
[tex]1.\ \angle GMT[/tex]
[tex]2.\ GT\ and\ TM[/tex]
[tex]3.\ \angle MGT[/tex]
[tex]4.\ SAS[/tex]
[tex]5.\ SAS[/tex]
[tex]6.\ SSS[/tex]
What is the measure of angle B in degrees?
Answers
Answer: how do I delete my answer?
Step-by-step explanation.
Here's the solution,
=》 C + 112° = 180°
( they form linear pair )
=》 C = 180° - 112°
=》C = 68°
And we know, measure of exterior angle if a triangle is equal to the sum of measures of the opposite interior angles,
So,
=》B = C + 51°
=》B = 68° + 51°
=》B = 119°
let g(x) = -2x+1. what is g'(3)? what is g'(4)?
Answers
Please help me with these 3 (last one is optional if you want to do it) but please don’t give me link to anything or you will get reported
Answers
Answer:
puedes o
Step-by-step explanation:
A farmer had 305 horses and 454 cows. Which of the following is a good
estimation of how many horses and cows he had altogether?
600 horses and cows
700 horses and cows
650 horses and cows
750 horses and cows
850 horses and cows
Answers
A farmer had 305 horses and 454 cows. Which of the following is a good estimation of how many horses and cows he had altogether?
600 horses and cows
700 horses and cows
650 horses and cows
750 horses and cows
850 horses and cows
____________________Solution :-Given Information :-Number of horses ➢ 305Number of cows ➢ 454 To Find :-Which of the following is a good estimation of how many horses and cows he had altogether?
600 horses and cows
700 horses and cows
650 horses and cows
750 horses and cows
850 horses and cows
Calculation :-Here, We will simply add up the number of animals ( cows and horses ) and then we will round it off to it's nearest 'tens' places.
⇒ Total number of animals = number of horses + number of cows
Substituting the values given, We get,
⇒ Total number of animals = 305 + 454
⇒ Total number of animals = 759
Now, when we round it off to it's nearest 'tens' places, We get,
⇒ Round off 759 = 750
Since, We can see that, 4th option from the list of option given, is 750. Therefore 750 is the answer.
____________________Final Answer :-4th option :- 750 horses and cows is the correct answer.____________________