[tex]Given \: cotA = \sqrt{\dfrac{1}{3}}[/tex]

Find all other trigonometric ratios. ​

[tex] \tt cotA = \sqrt{ \dfrac{1}{3}}[/tex]

[tex] \tt \implies cotA = \dfrac{1}{\sqrt{3}}[/tex]

All other trigonometric ratios, which are :

Let's make a diagram of right angled triangle ABC.

Now, From point A,

AC = Hypotenuse

BC = Perpendicular

AB = Base

[tex] \tt We \: are \: given, \: cotA = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt We \: know \: that \: cot \theta = \dfrac{base}{perpendicular}[/tex]

[tex] \tt \implies \dfrac{base}{perpendicular} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies \dfrac{AB}{BC} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies AB = 1x \: ; \: BC = \sqrt{3}x \: (x \: is \: positive)[/tex]

Now, by Pythagoras' theorem, we have

AC² = AB² + BC²

[tex] \tt \implies AC^{2} = (1x)^{2} + (\sqrt{3}x)^{2}[/tex]

[tex] \tt \implies AC^{2} = 1x^{2} + 3x^{2}[/tex]

[tex] \tt \implies AC^{2} = 4x^{2}[/tex]

[tex] \tt \implies AC = \sqrt{4x^{2}}[/tex]

[tex] \tt \implies AC = 2x[/tex]

Now,

[tex] \tt sin \theta = \dfrac{perpendicular}{hypotenuse}[/tex]

[tex] \tt \implies sinA = \dfrac{BC}{AC} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}x}{2x} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}}{2} [/tex]

[tex] \Large \boxed{\tt sinA = \dfrac{\sqrt{3}}{2}} [/tex]

[tex] \tt cos \theta = \dfrac{base}{hypotenuse}[/tex]

[tex] \tt \implies cosA = \dfrac{AB}{AC} [/tex]

[tex] \tt \implies cosA = \dfrac{1x}{2x} [/tex]

[tex] \tt \implies cosA = \dfrac{1}{2} [/tex]

[tex] \Large \boxed{\tt cosA = \dfrac{1}{2}} [/tex]

[tex] \tt tan \theta = \dfrac{perpendicular}{base}[/tex]

[tex] \tt \implies tanA = \dfrac{BC}{AB} [/tex]

[tex] \tt \implies tanA = \dfrac{\sqrt{3}x}{1x} [/tex]

[tex] \tt \implies tanA = \sqrt{3}[/tex]

[tex] \Large \boxed{\tt tanA = \sqrt{3}}[/tex]

[tex] \tt cosec \theta = \dfrac{hypotenuse}{perpendicular}[/tex]

[tex] \tt \implies cosecA = \dfrac{AC}{BC} [/tex]

[tex] \tt \implies cosecA = \dfrac{2x}{\sqrt{3}x} [/tex]

[tex] \tt \implies cosecA = \dfrac{2}{\sqrt{3}}[/tex]

[tex] \Large \boxed{\tt cosecA = \dfrac{2}{\sqrt{3}}}[/tex]

[tex] \tt sec \theta = \dfrac{hypotenuse}{base}[/tex]

[tex] \tt \implies secA = \dfrac{AC}{AB} [/tex]

[tex] \tt \implies secA = \dfrac{2x}{1x} [/tex]

[tex] \tt \implies secA = 2[/tex]

[tex] \Large \boxed{\tt secA = 2}[/tex]

[tex]\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(3,0){2.5cm}}\put(0,0){\line(0,3){2.5cm}}\qbezier(12.4,0)(6.6,5)(0,12.4)\put(-2,13){\sf A}\put(13,-2){\sf C}\put(-2,-2){\sf B}\put(-3,6){\sf 1}\put(6,-3){\sf \sqrt3$}\put(7,7){\sf 2}\end{picture}[/tex]

Given ,

We need to find ,

First finding the other side of the triangle using Pythagoras theorem .

Hypotenuse² = Base² + Height²

[tex]\to\sf Hypotenuse^2 = (1)^2 + (\sqrt3)^2[/tex]

[tex]\to\sf Hypotenuse^2 = 1 + 3 [/tex]

[tex]\to \sf Hypotenuse = \sqrt4[/tex]

[tex]\to\bf Hypotenuse = 2[/tex]

Now ,

Translate this sentence into an equation.
152 is the product of Vanessa's height and 8.
Use the variable y to represent Vanessa's height.

which expression is equivalent to 1/sin(2x) - cos(2x)/sin(2x)

help pls thanks guys

6. Calculate the slope of the line given the two points: (4,9) and (7,11).

Find the value of x​

There is a spinner with 12 equal areas, numbered 1 through 12. If the spinner is spun
one time, what is the probability that the result is a multiple of 5 and a multiple of 2?

If r+9=42 does r+9-9=42+9

Your friend first multiplies each side of 1/2 (x-9)=3/4 (5x+1) by 4 when solving the equation. Why might your friend do this?

PLEASE HELP NOW!! thanks:))

I WILL GIVE YOU THE BRAINIEST!!!

In a​ company, 60% of the workers are Men. If 2,320 people work for the company who​ aren't men, how many workers are there in​ all?

If Right.

15-18, use the properties of the exponents to write an equivalent expression for each given expression.


15. (4⁴)³



16. 3¹²
3³



17. 4⁵ • 4²



18. 6⁴ • 2⁴











please help!
​

Will mark brainliest for whoever answers

Please help and show how you got to the answer!

Please help
What is the inverse of the function f(x) = 4x + 8?

Evaluate
41+31
21
Answers 10’ 8’ 15

Solve -(10x + 1) + 4(x- 1) = -23

what does nani mean?

Find the circumference and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if
necessary.

GEOMETRY HELP PLEASE

Select all the rates that are unit rates.

1. [tex]\frac{1}{1/3}[/tex]

2.[tex]\frac{2/3}{1}[/tex]

3. [tex]\frac{2}{3}[/tex]

4. [tex]\frac{3}{1}[/tex]

5. [tex]\frac{1}{9}[/tex]

Please help me im confused on what I do here..

can someone help with this?

What is an equation of the line that passes through the point (2,-5) and is parallel
to the line 6x +y = 6?

The measure of an angle is nine times the measure of its complementary angle. What is the measure of each angle?
Will give 15 points plus Brainliest if your answer is correct!

4x - 2(x - 4) = -8 + 4x +4
solve the equation please

How many inches are in 2miles?

I am really bad at math! So can someone please help me again!

Rice yield prediction with Simple Linear Regression A simple linear regression is fitted to predict the yield of rice (kg per hectare) by using the annual rainfall (in mm) during the year. The intercept and slope of the regression equation are 473 and 5, respectively. What is the predicted rice yield if the annual rainfall is 582 mm? Choose an answer The predicted rice yield is: 2274 kg. Per hectare 1667 kg. Per hectare 3383 kg. Per hectare 2356 kg. Per hectare

At a football game, $3,114 is collected for tickets. General Seating admission tickets are $10 while Reserved Seating tickets cost $18. A total of 245 tickets were sold. How many tickets of each type are sold?

At Admiral Middle School there are 350 lockers in Hallway B, numbered 1 – 350. All of the
lockers are closed. Student #2 decides to run through Hallway B and opens every locker that is a
multiple of 2. Student #3 runs through and changes the state of every locker that is a multiple of 3 (if
it is open, he closes it. If it is closed, he opens it). Then student #4 runs through the hall and changes
the state of every locker that is a multiple of 4. Finally, student #5 changes the state of every locker
that is a multiple of 5. How many lockers are open after student #5 runs through Hallway B?

Express 80% as a percent as a decimal