ANSWER AND GET 30 POINTS!!! ASAP!!!
Which of the following are trigonometric identities? Select all that apply. (3)
What is a simplified form of the expression sec^2 x-1/sinx secx?
Answers
Answer:
1. A, E
2. C
Step-by-step explanation:
1. tan theta = 1/cot theta
sec theta = 1/ cos theta
2. Sec^2x-1 = tan^2x
sinx sec x = tanx
= tan^2x/tanx = tan x
The identities are (a) tan(θ) = 1/cot(θ), (c) 1 - sin^2(θ) = cos^2(θ) and (e) sec(θ) = 1/cos(θ) and the simplified form of [tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex] is tan(x)
Part A: The trigonometry identitiesAs a general rule, we have:
tan(θ) = 1/cot(θ)
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
sin^2(θ) + cos^2(θ) = 1
The above means that:
(a) tan(θ) = 1/cot(θ), (c) 1 - sin^2(θ) = cos^2(θ) and (e) sec(θ) = 1/cos(θ) are identities
Part B: The trigonometric proofWe have:
[tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex]
Express the numerator as tan^2(x)
[tex]\frac{\tan^2(x)}{\sin(x)\sec(x)}[/tex]
The product sin(x)sec(x) = tan(x).
So, we have:
[tex]\frac{\tan^2(x)}{\tan(x)}[/tex]
Divide
tan(x)
Hence, the simplified form of [tex]\frac{\sec^2(x) - 1}{\sin(x)\sec(x)}[/tex] is tan(x)
Read more about trigonometry ratios at:
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Related Questions
help
What is the domain and range of the exponential graphed below?
A.Domain: All real numbers
Range: y > -4
B.Domain: All real numbers
Range: All real numbers
C.Domain: x > 0
Range: y < -6
D. Domain: All real numbers
Range: y > 0
Answers
Answer:
B
Step-by-step explanation:
I just did the test
The range and domain of the function exists on all real values
Domain and Range of functionsDomain of a function is the value of the input of graph for which the function exists.
The range of a function is the value of the output of graph for which the function exists.
The given graph denotes an exponential function showing the arrow pointing infinitely in both directions. Hence the range and domain of the function exists on all real values
Learn more on range and domain here: https://brainly.com/question/2264373
A game is played with the following rules. Three ordinary coins are flipped and count as a single "turn" in the game.
Each coin could land on heads or tails. After their turn a player is given a certain number of points depending on the
outcome.
•If the result is 3 heads, the player receives +4 points.
• If the result is 2 heads, the player receives +2 points.
• If the result is anything else, the player receives -1 point.
What is the expected value of the number of points a player will receive after a turn?
Answers
=======================================================
Explanation:
H = heads
T = tails
Something like HHT means we get two heads in a row at first, followed by one tail. The order matters. Since there are 2 sides per coin, and 3 coins, this leads to 2^3 = 8 different possible ways to flip three coins.
Those 8 outcomes are:
HHHHHTHTHHTTTHHTHTTTHTTTAgain the order matters.
------------
Now let's define the following events
A = event of getting three headsB = event of getting exactly two headsC = event of getting 1 head, or getting 0 headsThere's only one way to get three heads, and that's HHH. So P(A) = 1/8.
There are three ways to get exactly two heads. Those three ways are: HHT, HTH, THH. This means P(B) = 3/8.
From those two probabilities, we then know that P(C) = 4/8 = 1/2 since there are 1+3 = 4 ways to get two or more heads, leaving 8-4 = 4 ways to get the other situations.
Now let's define function notation V(A) to mean "the net value of event A occurring". It's the number of points you receive if event A happens. We are given the following info:
V(A) = 4V(B) = 2V(C) = -1From here, multiply the probability values with their corresponding net values
P(A)*V(A) = (1/8)*(4) = 0.5P(B)*V(B) = (3/8)*(2) = 0.75P(C)*V(C) = (1/2)*(-1) = -0.5Finally, add up those results to get the expected value: 0.5+0.75+(-0.5) = 0.75
Each time a turn happens, we expect on average to get 0.75 points
Imagine a scenario where you play the game 10,000 times. If you record the result of each turn and then compute the arithmetic mean, you should get somewhere close to 0.75; it likely wont be 0.75 exactly due to the nature of theoretical probability and empirical probability not being perfectly aligned. However, due to the law of large numbers, the two should be very close when you do a large number of trials.
Because we're dealing with averages, it is possible to get a decimal value as the answer even though the point values of events A,B,C are integers.
pls help thank you so much !!
Answers
Answer:
a) (0,5)
Step-by-step explanation:
Question 14 of 15
Evaluate (3/4)x^0
Answers
Answer:
I'm not sure if this is right, but I got 3/4. (0.75 as a decimal) I hope this helps!
Step-by-step explanation:
Decimal form: 0.74
Select the correct answer
Answers
Answer:
x = 95°
y = 147°
z = 128°
Step-by-step explanation:
z = 180 - 52 = 128°
x: first find the remaining angle in the big triangle, 180 - (45 + 50) = 85°
x = 180 - 85 = 95°
y: first find the remaining angle in the small triangle, 180 - (95 + 52) = 33°
y = 180 - 33 = 147°
Use the following function rule to find f(3).
f(x) =
8
x
+ 9
f(3) =
Answers
Answer:
f(3)= 33
Step-by-step explanation:
hello :
f(x) =8x+9
put x = 3 you have : f(3) =8(3)+9 = 24 + 9 =33
Need help on this one last question
Answers
Answer:
available
Step-by-step explanation:
if its available if available comment
bakit mahalagang matutunan ang mga angkop na pahayag sa panimula gitna at wakas mg isang akda
Answers
Answer:
i understand your statement my good sir but, what is the question?
Step-by-step explanation:
Last month a bakery sold a total of 3,500 cookies and cupcakes. They sold cookies for $0.75 each and cupcakes for $2 each. If the total sales last month was $4,500, how many cookies and how many cupcakes did the bakery sell?
Answers
Answer:
Number of cookies sold is 2000 and number of cupcakes sold is 1500
Step-by-step explanation:
Let number of cookies be [tex]x[/tex]
and number of cupcakes be [tex]y[/tex] so
[tex]x+y=3500[/tex]
Cost of one cookie is $0.75
Cost of one cupcake is $2
[tex]0.75x+2y=4500[/tex]
[tex]x+y=3500[/tex] [tex]\times 2[/tex]
[tex]2x+2y=7000[/tex]
[tex]-1.25x=-2500\\\Rightarrow x=\dfrac{2500}{1.25}\\\Rightarrow x=2000[/tex]
[tex]y=3500-x=3500-2000\\\Rightarrow y=1500[/tex]
Number of cookies sold is 2000 and number of cupcakes sold is 1500.
Will give brainiest help please
Write the equation of the line in Slope-Intercept Form.
(-2,3),(0,-1)
Answers
11. A rectangle has a diagonal of length 10 units and one side of length 6 units.
How many units long is the perimeter of the rectangle?
Answers
10 + 10 + 6 + 6 = 32
The required perimeter of the rectangle is 28 units.
What is a rectangle?
The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
Let's denote the length of the rectangle as L and the width as W. We know that the diagonal of the rectangle has a length of 10 units, and we can use the Pythagorean theorem to relate the length, width, and diagonal,
L² + W² = diagonal² [= 10² = 100]
We also know that one side of the rectangle has a length of 6 units, which we can assume is the width W. Therefore, we can solve for the length L,
L² + 6² = 100
L² = 100 - 36
L² = 64
L = 8
So the length of the rectangle is 8 units.
To find the perimeter of the rectangle, we can use the formula P = 2L + 2W, where L is the length and W is the width:
P = 2(8) + 2(6)
P = 16 + 12
P = 28
Therefore, the perimeter of the rectangle is 28 units.
Learn more about rectangles here:
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evaluate 5^28·5^-32·5^-4
A. 17,920
B. 0.017920
C. 0.000256
D. 0.00000256
Answers
Answer:
D 0.00000256
Step-by-step explanation:
[tex]5^{28} *5^{-32}*5^{-4}=5^{28-32-4}=5^{-8}=\frac{1}{5^{8}} =0.00000256[/tex]
Answer:
B. 0.000256
Step-by-step explanation:
5^28 . 5^- 32 . 5^ -4
= 5^( 28 - 32 - 4 )
= 5^( 28 - 36 )
= 5^- 8
= 1 / 5^8
= 1 / 390625
= 0.000256
The sum of Derek and Quency's ages is 19 years. If the difference
of their ages is 5 years what are their ages?
Answers
hope this helped
Solve for n: 5n - 7= -52 A. - 5 B. -9 c. - 5/45 D. 9 E. 26
Answers
Answer: n= -9
Step-by-step explanation:
5n-7=-52
5n = -52+7
5n=-45 (divide both sides)
n= -9
The ages of six boys are given as 12years 3 months,18years 10months,18years 8months,13years 4months,17years 11month and 15years respectively, what is their average age?
Answers
12+0.25+18+0.83+13+0.333+17+0.916+15=77.326
77.326/11=7.029 which rounds to 7
Consider this right triangle...
Omg pleaseeeee help me!! I have SBA Math Test on Friday and I forgot everything I learned last year from Geo. Help would be very very much appreciated!! WILL GIVE BRAINLIEST!! Thank you so muchhhhh <3
Answers
Answer:
33°
Step-by-step explanation:
have a nice day!! :)
I need Help please!!
Answers
solve the equation-4(x+10)-6=-3(x-2)
Answers
Answer: x= -52
Step-by-step explanation:
What is the solution to follow system of equations?
x-3y=7
2x-6y=12
Answers
At a glass vase factory, 2 out of the last 20 vases produced were chipped. Considering this data, how many of the next 10 vases would you expect to be chipped?
Answers
2 out of 20 = 2/20 which reduces to 1/10 which means 1 out of every 10.
I would expect 1 out of the next 10 to be chipped.
Answer:
1
Step-by-step explanation:
Does anyone know which answer it is in the image? Doesn’t require any work
Answers
Answer:
b
Step-by-step explanation:
Answer:
It's the second one
If each serving of the stew will contain 1 4 14 pound of meat, how many servings of the stew can the club make? Enter your answer in the box.
Answers
Complete question :
The line plot shows the weights of packages of meat that members of a club bought. The meat will be mixed with vegetables to make stew for a club dinner. Each serving of the stew contains 1/4 pound of meat. How many servings of the stew can the club make?
Answer:
36 servings
Step-by-step explanation:
From the plot ; we take the sum of total weight of meat packages :
(5/8 * 2) + 6/8 + 1 + (9/8 * 3) + 10/8 + 11/8
10/8 + 6/8 + 8/8 + 27/8 + 10/8 + 11/8 = 72 / 8 = 9 meat packages
Each serving of meat = 1/4
Number of servings the club can make :
Total meat package / pound of meat per serving
(9 ÷ 1/4)
9 * 4/1
= 36 servings
Answer:
36 hope this help
Step-by-step explanation:
what inequality is equivalent to 2/3x - 5 <11 ?
Answers
Find ∠L using law of sines
Answers
Answer:
29°
Step-by-step explanation:
:)
Please help!!
Find the radius
Answers
Answer:
The radius is 20 units.
Step-by-step explanation:
(r)^2 + 21^2 = (r+9)^2
r^2 + 441 = r^2 + 18r + 81
360 - 18r = 0
360 = 18r
20 = r
please help
if your gonna scam just leave i really need help
Answers
Answer:
x = 23
Step-by-step explanation:
The measures of the angles in a triangle add up to equal 180
That being said we can create an equation to solve for x
180 = 2x + 3x + 1 + 3x - 5
Now we solve for x using basic algebra
step 1 combine like terms
2x + 3x + 3x = 8x
1 - 5 = -4
now we have 180 = 8x - 4
step 2 add 4 to each side
-4 + 4 cancels out
180 + 4 = 184
now we have 184 = 8x
step 3 divide each side by 8
8x/8=x
184/8=23
we're left with x = 23
What is the probability of landing on a 9 and then landing on a 7?
Answers
Answer:
what are we landing on? D 10s D20s?...
Step-by-step explanation:
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A rectangular garden has an area of 84 square feet and a length of 7 feet. What is the width of the garden?
Answers
Answer:
12 ft
Step-by-step explanation:
Given data
Area= 84 ft^2
Length= 7ft
The expression for the area is
Area= L*W
substitute
84=7*W
W= 84/7
W= 12ft
Hence the width is 12 ft
Answer:12ft
Step-by-step explanation:
Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.
Which is the best estimate for the amount of money Megan has left?
Answers
Answer:
Hello Love!
A good estimate would be 15 or 16 dollars left
Hope this helps!
Answer:
$15.98
Step-by-step explanation:
45.12-7.89=37.23
37.23-21.25=15.98
A submarine started 30 feet below the surface of the water. It is now 10 feet below the surface. What integer represents the change in depth?
Answers
Answer:
-20 feet
Step-by-step explanation:
change in depth = number of feet below the surface + number of depth on the surface
Because the submarine is below surface, a value of -30 would be given
-30 + 10 = -20 feet
