Given [tex]cot(\alpha )=-\sqrt{3}[/tex] and [tex]\pi/2 \ \textless \ \alpha \ \textless \ \pi[/tex], find the exact values of the five remaining trigonometric functions:
1. [tex]sin(\alpha )[/tex]
2. [tex]cos(\alpha )[/tex]
3. [tex]tan(\alpha )[/tex]
4. [tex]csc(\alpha )[/tex]
5. [tex]sec(\alpha )[/tex]

Answers

Answer 1

Immediately, by definition of cotangent, we find

tan(α) = 1/cot(α) = 1/(-√3)

⇒   tan(α) = -√3

Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.

Recall the Pythagorean identity,

cos²(α) + sin²(α) = 1

Multiplying both sides by 1/sin²(α) recovers another form of the identity,

cot²(α) + 1 = csc²(α)

Solving for csc(α) above yields

csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4

⇒   csc(α) = 2

⇒   sin(α) = 1/2

Solve for cos(α) using the first form of the Pythagorean identity:

cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)

⇒   cos(α) = -√3/2

⇒   sec(α) = -2/√3


Related Questions

What is the vertical shift for the absolute value function below. Explain how you know using complete sentences. Include the direction and number of units of the shift. f(x)=9|x+1|+2

Answers

The vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

The absolute function is given as:

[tex]f(x) = 9|x + 1| + 2[/tex]

An absolute function is represented as:

[tex]f(x) = a|x - h| + k[/tex]

Where k represents the vertical shift.

By comparison, the value of k is:

[tex]k = 2[/tex]

This means that the vertical shift is 2 units

Hence, the vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

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Henry jumped up 6 steps. Each step was 3/10 feet high. How high did he jump all together (in simplest form)

Answers

Answer:

1.8 or 14/5

Step-by-step explanation:

HENry MuST Be A KaNGaRoO

Answer:

Step-by-step explanation:

Multiply "3/10 ft high per step" by "6 steps."  This works out to:

18/10 ft was the highest that this young man jumped.

This reduces to 9/5 ft, or 1.8 ft

three movie tickets cost 36$ at this same rate how much do 12 tickets cost

Answers

Answer:

$144

Step-by-step explanation:

Each ticket is $12.

138.4divided by16 show works it possible to show your work

Answers

Ok done. Thank to me :>

How do you use observed data to predict unobserved

Answers

You can determine that the test scores will drop with more hours of tv watched. Though as you can also notice there seem to be more outliers later in the data so you can determine that what is I observed will have more outliers than what is observed.

Determine the number of solutions you will have for the system 4y + x = 16 and y = 4 – x.

Answers

Equaling both equations, it is found that the correct option that states the number of solutions you will have for the system is:

D: one solution

The equations are:

[tex]4y + x = 16 \rightarrow x = 16 - 4y[/tex]

[tex]y = 4 - x \rightarrow x = 4 - y[/tex]

Equaling both equations for x, we have that:

[tex]16 - 4y = 4 - y[/tex]

[tex]3y = 12[/tex]

[tex]y = \frac{12}{3}[/tex]

[tex]y = 4[/tex]

[tex]x = 4 - y = 4 - y = 0[/tex]

Hence, the system has one solution, which is (0,4), and option d is correct.

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Help help help help help m at h math math

Answers

Answer:X= 6X-14

Step-by-step explanation:

Exercise on Properties/Laws of Sets Simplify each of the following identities to its simplest form, using the laws of sets; (i) (An B) U (AU B')'
(ii) An (AUB)
(iii) (CUA N (BUA)​

Answers

bro wat like bro what like what what bro.



help with this question, please!

Answers

Answer:

Y Intercept: 0, 2.5

X Intercept: 3.5, 0

Explanation:

An Intercept is where a line crosses an axis. A Y Intercept is for the Y axis and the X intercept is for the X axis.

Also when writing coordinates, the x coordinate comes before the y one.

Hope this helps :)

I WILL GIVE BRAINLEST AND 60 POINTS I KNOW ITS NOT ALOT
Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.




2. How many times did Melanie run ½ a mile?

Answers

Answer:

Melanie and 2 times ½ a mile

Hopes This helps

write an expression that shows 9 less than the product of 11 and 3.5

Answers

try this for answer (11×3.5)-9=x

Find the length of the third side. If necessary, round to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

a² + b² = c²

12² + b² = 15²

b² = 225 - 144

b² = 81

b = 9

Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What is the price of one chair? Use the drop-down menus to complete parts A and B below.

Answers

The price of one chair Ben bought is $80 and he bought 6 chairs in total.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.

Assuming each chair costs $x and his total cost is $720.

240 + 6x = 720.

6x = 720 - 240.

6x = 480.

x = 80

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3x+5y−7x+6=12
Calculate.Solve for x.​

Answers

The value of x from the equation is x = (5y - 6)/4

Given the equation 3x+5y−7x+6=12

collect the like terms;

3x-7x + 5y + 6=12

-4x + 5y = 12 - 6

-4x + 5y = 6

Subtract 6 from both sides

-4x + 5y - 5y = 6 - 5y

-4x = 6 - 5y

4x = 5y - 6

x = (5y - 6)/4

Hnce the value of x from the equation is x = (5y - 6)/4

learn more on subject of formula here: https://brainly.com/question/657646

It takes 10 hours to type 4 reports how many hours does it take to type 15 reports

Answers

Answer:37.5 hrs

Step-by-step explanation:

15/4 = 3.75

3.75*10=37.5

The answer is 37.5 hours

If Y = 13 inches, Z = 19 inches, H = 7 inches, and W = 3 inches, what is the area of the object?
A.
304 square inches
B.
123.5 square inches
C.
147 square inches
D.
190 square inches

Answers

Answer:

Step-by-step explanation:

Ask Siri

13,22,31,...
Find the 31st term.
Find the 31st term.


Answers

Answer: 283

Step-by-step explanation:

To do this, it is helpful to get an equation you can use to solve any term.

This equation is:

[tex]13 + 9(n-1)[/tex]

So simply plug in 31 for n to get

[tex]13+9(31-1)[/tex]

[tex]=13+270[/tex]

[tex]=283[/tex]

Answer:

283

Step-by-step explanation:

9x+4=9(31)+4=283

13+9=22

22+9=31

9x

9(1)=9 9+4=13

9x+4

can you help me with this graph question ​

Answers

4,-5
explaination: sorry if not correct!

Answer:

D

Step-by-step explanation:

the Max Point is (2,6) so y=b

sorry if u dont get it

Find the value of sin D rounded to the nearest hundredth, if necessary.

Answers

Answer:

0.22

Step-by-step explanation:

So in this problem, we have to find the hypotenuse first, since sine is opposite over hypotenuse.

We can do this using the pythagorean theorem (you can search it if you don't know). Or, we can just remember this as one of our pythagorean triplets (9,40,41). The last side will be 41.

We have to find the value of sin(D)

opposite/hypotenuse = 9/41 = 0.2195 which is about 0.22

Planes A and B are shown.
If a new line, p, is drawn parallel to line I, which
statement is true?
ZA
O Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line 1
O Line p must be drawn in the same plane as line n.
m

Answers

B. line p must be tge perpendicular to line M

will give brainly if you help me thx

Answers

Answer:

A

Step-by-step explanation:

The answer is A because is it asking for a 3 in the hundredths place of the difference. Difference means subtraction. And you can find the hundredth spot in the second place over from the decimal

(ex. 1.23, hundredth place is a 3)

So then you do the math and find the differences.

14.56-9.33=5.23, which has a 3 in the hundredth place.

A TON OF POINTS AND BRAINLIEST IF ANSWERED CORRECTLY! I RLY NEED HELP PLZZZ ANSWER

Use the function f(x) = 2x^2 − 3x − 5 to answer the questions.

Part A: Completely factor f(x). (2 points)

Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)

Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

Answers

Answer:

Step-by-step explanation:

For  

f(x) = 2x2-3x -5

For Part A

Set f(x) = 0

Factor the Quadratic

Set the factors = 0  

Solve each factor for x to find your x intercepts

For Part B

You need to use the coefficients in your Quadratic  

List them

a = 2 , b = -3 and c = -5

Since a is positive, your parabola opens up  

Find the x coordinate of the vertex it is -b/2a

One you get the x coordinate, plug it into to your Quadratic to get f(x) your y coordinate of the vertex

For Part C

You can plot the vertex, both x intercepts on a coordinate grid

Two angles are supplementary. The smaller angle is 35 degrees less than the larger angle. What is the measurement of the larger angle?

Answers

Answer:

Step-by-step explanation:

1. The total amount of what you eam during the pay period before taxes and deductions are taken out is known as what?
Wage
Net pay
Salary
Gross pay

Answers

Answer:

net pay if im not mistaking

Step-by-step explanation:

please help ill mark brainliest​

Answers

Answer:

I think its A ratio reduced, since a scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Answer:

It isn't either of the first two. My best guess would be the units of a ratio, (sorry if it's actually a ratio reduced). It's worded very weirdly

of the negative number, and of the
16
6 The sum of a negative number,
negative number is – 13.2. What is the negative number?

Answers

Answer:

semoga jawabannya benar

Step-by-step explanation:

Korelasi Rank Spearman digunakan untuk mencari hubungan atau untuk menguji signifikansi hipotesis asosiatif bila masing-masing variabel yang dihubungkan berbentuk Ordinal.

Answer:

179.2

Step-by-step explanation:

166 = x + -13.2

166 - -13.2 = 166 + 13.2 = 179.2

Mark purchased a 20 foot long sub for a party he cuts the sandwich into 5/12 foot sections into how many pieces does he cut the sandwich

Answers

Answer:

48 pieces

Step-by-step explanation:

20÷5/12=20*12/5=240/5=48

PLEASE HELP ME




Question 7 of 10

Which of the following is equal to the fraction below? (5/9)⁸

A. 5⁸/9⁸

B. 5/9⁸

c. 5⁸/9

D. 8•(5/9)

SUBMIT

Answers

Answer:

A 5⁸/9⁸

Step-by-step explanation:

the bracket there shows that the power is for both the numerator and denominator so A is the correct answer

I need help with this

Answers

Answer:    y = (-5/4)x - 8

========================================================

Explanation:

Recall that y = mx+b is the slope intercept form of any linear equation

m = slopeb = y intercept

The given equation has m = 4/5 as the slope. Flip the fraction to get 5/4 and then flip the sign to get -5/4

The original slope is 4/5 and the perpendicular slope is -5/4. Note how the slopes multiply to -1.

The slope for the answer is -5/4 and the y intercept for the answer is -8

Therefore, the perpendicular line is y = (-5/4)x - 8

i’m 70% sure it’s y=-5/4x -8

Which of the segments below is a secant?
С
F
О.
В
Д.
А
u
А. ОВ
B. AB
ООО О
C. DE
D. AD

Answers

Answer:

it is d i believe

The secant of a circle is line segment AD. Therefore, option C is the correct answer.

What is secant of a circle?

A line that crosses a circle at two different locations is said to be a secant of the circle. The Roman verb secare, which meaning to cut, is the source of the word secant. It can also be thought of as the chord of a circle extended outside of the circle.

Given that, circle with center O.

In the given figure, FC is chord, OB is radius, AB is tangent, AD is secant and DE is tangent.

Therefore, option C is the correct answer.

Learn more about the secant of a circle here:

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