Please help with any of this Im stuck and having trouble with pre calc is it basic triogmetric identities using quotient and reciprocal identities
Answers
How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.
#3
Let's start with sin here. [tex]\frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}}[/tex] Therefore, because sin is y/r, r = [tex]\sqrt{5}[/tex] and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.
cos = [tex]\frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}[/tex]
#4
Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = [tex]4\sqrt{2}[/tex]. Now, to find csc, we have to do r/y.
csc = [tex]\frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}[/tex]
The pythagorean identities are
sin^2 + cos^2 = 1,
1 + cot^2 = csc^2,
tan^2 + 1 = sec^2.
#5
Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.
sin^2 + (-3/4)^2 = 1
sin^2 + 9/16 = 1
sin^2 = 7/16
sin = [tex]\sqrt{7/16}[/tex] = [tex]\frac{\sqrt{7}}{4}[/tex]
Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.
tan^2 + 1 = (-4/3)^2
tan^2 + 1 = 16/9
tan^2 = 7/9
tan = -[tex]\sqrt{7/9} = \frac{-\sqrt{7}}{3}[/tex]
#6
Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.
1 + cot^2 = [tex](\frac{-\sqrt{6}}{2})^{2}[/tex]
1 + cot^2 = 6/4
cot^2 = 2/4
cot = [tex]\frac{\sqrt{2}}{2}[/tex]
tan = [tex]\sqrt{2}[/tex]
Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.
[tex](\frac{2}{\sqrt{2}})^2[/tex] + 1 = sec^2
4/2 + 1 = sec^2
2 + 1 = sec^2
sec^2 = 3
sec = -[tex]\sqrt{3}[/tex]
cos = [tex]\frac{-\sqrt{3}}{3}[/tex]
Hope this helps!! :)
Answer:
sin(θ)=√7/4
tan(θ)= - √7/3
Step-by-step explanation:
c^2= √(4^2-(-3^2))
c^2= √(16-9)
c^2= √7
sin(θ)= opp/hyp=√7/4
tan(θ)= (opp )/adj= - √7/3
Related Questions
what is the area to this triangle
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Answer:
12 x 12 = 144 divided by 2 = 72, 72 is your answer formula of a triangle: BH x 1/2
Step-by-step explanation:
72 square cm
find the area of the figure?
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Answer:21
Step-by-step explanation:
you draw a line so there a grid measured 5 by 3 and a grid measured 2 by 3.
P(x)=0.2x^2+20x-4 where x is the number of units sold. How many units need to be sold for the business to make a profit of $101?
Answers
Answer:
5
Step-by-step explanation:
Given the profit equation ;P(x)
x = number of units sold
P(x) = profit made
P(x) = 101
101 = 0.2x^2+20x-4
0.2x^2+20x-4 - 101
0.2x² + 20x - 105 = 0
Using the formula:
-b±[sqrt(b² - 4ac) / 2a]
Where ;
a = 0.2 ; b = 20, c = - 105
Using the quadratic equation solver to save time :
The roots are :
-105 and 5
Items sold cannot be negative ;
Hence, x = units sold = 5
im stuck on this question
Answers
Answer: f
Step-by-step explanation: I chose f because m=29.57 which is is the starting point
I NEED HHELLLPPPPPPPPPPPPPPPPPPPPP
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Answer:
10.6
Step-by-step explanation:
Answer:
x = 122°
Step-by-step explanation:
since it is a right triangle, the sum of the other 2 interior angles = 90°
the angle opposite x = 90° - 32° = 58°
58° and angle x are supplementary angles. Their sum is 180°.
180° - 58° = 122°
5
A rectangle has a width that is 5 feet less than the length. The area of the rectangle is
126 square feet. Find the width of the rectangle. (Do not type units in the answer)
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Answer:
Step-by-step explanation:
Alyssa uses 4 ounces of flour to make pancakes each morning how long will it take her to use up a 6 pound bag
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If Alyssa uses 4 ounces of flour to make pancakes each morning how long will it take her to use up a 6 pound bag is 24 days.
Number of daysUsing this formula
Number of days=Number of ounces×Number of pound bag
Where:
Number of ounces=4 ounces
Number of pound bag=6
Let plug in the formula
Number of days=4×6
Number of days=24 days
Therefore how long will it take her to use up a 6 pound bag is 24 days.\]
Learn more about number of days here:https://brainly.com/question/9286901
Simplify√60×√180/√75
Answers
What is the exponential function (0,25) (1,50) (2,100) (3,200) (4,400)
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Answer:
Step-by-step explanation:
If it is exponential dividing any term by the preceding term will be a constant, the common ratio or rate. 50/25=100/50...=2 The initial value, a, (at x=0) is 25 so the general form is
y=ar^x we have a=25 and r=2 so
y=25(2^x)
I NEED HELP ASAP!!!
Do a conclusion and tell how or where you will use 3D shapes in the future.
Answers
Answer:
You will use 3D shapes in the future when creating blueprints for buildings and infrastructure.
HELP ASAP!! BEST ANSWER GETS BRAINLY! pls only answer if u know the answer this is a test!
Which answer is the slope-intercept form for the given equation? 1/3x+2y=4/3
y=2/3x+4/3
y=−1/6x+4/3
y=−2/3x+2/3
y=−1/6x+2/3
Answers
Answer:
It's the fourth one y=-1/6x+2/3
Step-by-step explanation:
I have to study for a test. It's for data management. Does anyone have tips? (Grade 7)
Answers
Studying: Use resources.
If your studying for a test, use some resources, like quizizz, quizlet, flashcards, or the internet. If you do, ask your parents for help. Think it like its your big test, and your studying a lot. If you study and try, you'll pass the test on data management. If you need it, ask your teacher for tutoring or practice some data management questions. Studying will help you not to fail a test.
Now, we'll talk about before the test.
Before test: Rest, eat breakfast, and stay calm.
Step-by-step explanation: Going to bed before a test can prevent you from going to sleep. For example, GMAS (for me) is coming soon, and my teacher encourage us to rest, eat breakfast and stay calm. A recommended time for you to go to bed is 8:00-9:30.
Now, about breakfast.
Eating breakfast is also important because you can perform better, in fact, scientists say that if students eat breakfast before a test or exam, they will perform better! Whatever you do, don't skip breakfast. If you do, you won't perform good, and theirs a chance you could fail.
Now, staying calm is the big one.
If your freaking out, stay calm, say a prayer and get your work done! Staying calm is the big one because most students (I am one of them) get worried if they're gonna fail. Keep this in mind: Try. Your. Best. If you don't try, you won't achieve anything. And please don't cheat. If you cheat, you'll have to repeat the whole grade. Can't cheat in college; you'll get kicked out.
During test: DO. NOT. CHEAT.
CHEATING WILL GET YOU KICKED OUT OF COLLEGE AND YOU'LL AUTOMATICALLY FAIL!!! If your computer prevents you from going to other sites, that is good, but don't pull out ANY study guides or notes during your test, unless it's open-notes. If you don't know a questions, skip it and go to the next one. Then go back, it will come to mind later. If your done with your test early, check your answers. Look back and think, "Is this correct?"
Hope you do good on your test!
~ Lily, from Brainly.
what is pi and how invented it??
Answers
Answer:
Step-by-step explanation:
The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.
Answer:
π is a mathematical constant. Its commonly used value is 3.14. There is a expanded value for π. It appears in many formulas in all areas of mathematics and physics. In maths, it is commonly used for solving of circles and spheres.
The π was invented by Archimedes of Syracuse. He was one of the greatest mathematicians of the ancient world.
INSTRUCTIONS: Calculate the Mean, Median, Mode, and Range from the data set (February 14-28, 2021).
10.9, 10.4, 9, 5.7, 7.8, 9.3, 2.2, 11, 9.6, 4.8, 7.4, 8.4, 7.7, 10.8, 7.7, 10.8, 13.7 (PLS HELP)
Answers
Answer:
The mean is 128.7
There is no mode
The median is 9
The range is 11.5
Step-by-step explanation:
Help please
Brainiest answer to whoever is first
Answers
Answer:
75
Step-by-step explanation:
To make 12 ounces of hot chocolate, 3 tablespoons of cocoa are needed. How many tablespoons of cocoa are needed to make 72 ounces of hot chocolate?
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Answer:
18
Step-by-step explanation:
which is a rational number
a) 1.4142135623
b) 3.6256256
c) 2 (pie)
d) squared 5
Answers
Answer:
Rational numbers can be expressed as a fraction
Squared 5 = 25
25 can be expressed as a fraction- 25/1, so d is correct.
Let me know if this helps!
5 squared is right im sorry i miss read it
An item costs $420 before tax, and the sales tax is $25.20 . Find the sales tax rate. Write your answer as a percentage.
Answers
Answer:
6%
Step-by-step explanation:
Given data
Cost of item= $420
Tax= $25.2
Required
The tax rate
=25.2/420*100
=0.06*100
=6%
Hence the tax rate is 6%
there are 96 coins in a bottle
1/2 coins are $1 coins
rest of the coins are 50p coins
work out the total value of 96 coins
Answers
Answer:
The total value of the 96 coins is 72.
Step-by-step explanation:
There are half coins of 1. 48 coins of 1. It is cost will be 48. And rest are of 50p. 48 coins of 50 p. Therefore it is cost will be 24. The total cost will be 48+24=72.
Part 1: What is the rate of rice to quarts of water for this recipe that uses 4 pounds of rice and 5 quarts of boiling water?
Answers
Given:
A recipe uses 4 pounds of rice and 5 quarts of boiling water.
To find:
The rate of rice to quarts of water for this recipe.
Solution:
We need to divide the amount of rice by amount of water to get the rate of rice to quarts of water for this recipe.
[tex]\text{Required rate}=\dfrac{\text{Rice in pounds}}{\text{Water in quarts}}[/tex]
[tex]\text{Required rate}=\dfrac{4}{5}[/tex]
[tex]\text{Required rate}=0.8[/tex]
Therefore, the rate of rice to quarts of water for this recipe is 0.8.
A model of a statue has a height of 4 cm. The volume of the model is 12 cm3 . 3 The volume of the statue is 40 500 cm
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Answer:Pencil, pen, ruler, protractor, pair of compasses and eraser ... Work out the volume of prism B. me x3' (X27). 15X27 = 405. 405 ..cm3 ... 3. Below are two similar parallelograms. X1.5. 4cm / A /. 6cm. B. The area of ... bon Area: 120 cm? 3 ... Two clay models of the Statue of Liberty are mathematically similar.
Step-by-step explanation:
Sorry If It Dont Help But It Helped Meh...Come Back To Meh If Its Wrong♀️....
What is the distance between (4, 7) and (-8, 3)? Round to the nearest tenth.
Answers
Answer:
The distance is approximately 12.6.
Step-by-step explanation:
Moving from (-8, 3) to (4, 7), we see x (the horizontal dimension) increasing by 12 and y (the vertical dimension) increasing by 4. Think of 12 and 4 as the legs of a right triangle whose hypotenuse represents the distance between these two given points.
This distance, from the Pythagorean Theorem, is
d = √(12^2 + 4^2) = √(144 + 16) = √160 = √16√10.
The desired distance is approximately 12.6.
Find the solutions to the equation x2 - 15x - 100 = 0.
Answers
Answer:
X= 20 or -5
Step-by-step explanation:
What is the area of the rectangle, in square feet?
A rectangle with length 20 feet and width 9 feet.
29
58
120
180
Answers
Pleaseeeeee can anyone help me????
Answers
Answer:
27.63
Step-by-step explanation:
r = 4.4
Circumference of a Circle formula:
C = 2πr
C = 2(3.14)(4.4)
C = 6.28(4.4)
C = 27.632
Rounded to the nearest hundredth:
27.63
Answer:
C= 27.63 inches
Step-by-step explanation:
Use the circumference formula C = 2πr.
Subsitute what you are given into the equation and solve.
C = 2πr
C= 2*(3.14)*(4.4inches)
C= 27.63 inches
Stephanie wants to make 22.5 qt. of a 20%
alcohol solution by mixing together a 6%
alcohol solution and a 36% alcohol solution.
How much of each solution must she use?
Answers
Answer:
y = 10.5qt
x = 12 qt
Step-by-step explanation:
0.6x+ 0.36y = 22.5 * 0.2
0.06x + 0.36y = 4.5
x + y = 22.5
x = 22.5 - y
0.06(22.5 - y) + 0.36y = 4.5
1.35 - 0.06y + 0.36y = 4.5
0.3y = 4.5 - 1.35
0.3y = 3.15
y = 3.15 / 0.3
y = 10.5 qt
x = 22.5 - y
x = 22.5 - 10.5
x = 12 qt
Mariah is replacing the water heater in her home and is considering three different models. One of the things she is comparing is
the volume of the cylindrical storage tank in each water heater. The dimensions of the storage tanks, in inches, are as follows.
• Water Heater X: r= 8.5 and h = 48
• Water Heater Y: r= 9.5 and h = 44
• Water Heater Z: r= 10.5 and h = 32
Which statement is true?
OA. Water heater Y has the storage tank with the greatest volume.
B. Water heater X has the storage tank with the greatest volume.
OC
The storage tanks in all three water heaters have the same volume.
OD
Water heater Z has the storage tank with the greatest volume.
Answers
Answer:
A
Step-by-step explanation:
The volume of a Cylinder is [tex]\pi \\[/tex]*r^2 * h
In this problem I will use 3.14 as pi because it is easier to type
Water Tank X: 8.5*8.5*3.14*48=10,889.52
Water Tank Y: 9.5*9.5 *3.14*44=12,469.94
Water Tank Z: 10.5*10.5*3.14*32=11,077.92
So, A is correct.
Surface area
Please help!!
Math, surface area
Answers
Answer:Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. ... We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
https://youtu.be/sskf3tF2heU?t=8
A ship leaves the Port of Miami and travels due east toward the Bahamas for 3 miles. The ship turns due south and travels for some distance. The captain then looks back and determines that the ship is directly 10 miles from the starting point at the Port of Miami. How many miles did the ship travel south before the captain checked the distance to the Port of Miami? Round your answer to the nearest tenth. the
Answers
Help pls!!! question in the picture!!!
Answers
Answer:
The Y intercept is two
Step-by-step explanation:
The y intercept is the point on a graph where the graph crosses the y axis.
Basically, it is the value of y when x is 0 is (x,y)
Looking at the attached graph, our y intercept is (0,2), meaning that the y-intercept is 2.
The answer is: the Y-INTERCEPT is 2