Let θ be an angle in quadrant IV such that sinθ=-3/4. Find the exact values of secθ and cotθ.
Answers
cos2(θ) + sin2(θ) = 1
sec(θ) = 1/cos(θ)
cot(θ) = cos(x)/sin(θ)
sin(θ) = -3/4
cos2(θ) + sin2(θ) = 1
cos2(θ) = 1 - sin2(θ)
cos2(θ) = 1 - 9/16 = 7/16
cos(θ) = ±√(7/16) = √7/16 (cosine is positive in Q IV)
sec(θ) = 1/cos(θ) = 4/√7
cot(θ) = cos(θ)/sin(θ) = (4/√7)/(-3/4) = -16√7/21
The exact values of secθ = 4/√7 and cotθ = -16√7/21
What is Trigonometric functions?Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
Given that,
sinθ = -3/4
∵sin²(θ) +cos²(θ) = 1
∴cos²(θ) = 1 - sin²(θ)
cos(θ) = √(1 - sin²(θ))
cos²(θ) = √(1 - 9/16 )
cos(θ) = ±√(7/16) = √7/4 (cosine is positive in quadrant IV )
sec(θ) = 1/cos(θ) = 4/√7
∵cot(θ) = cos(θ)/sin(θ)
∴cot(θ)= (4/√7)/(-3/4)
cot(θ) = -16√7/21
The exact values of secθ = 4/√7 and cotθ = -16√7/21
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Related Questions
Which of the following is equivalent to
Answers
Answer:
1/6
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
3.) Calculate the volume of the rectangular prism shown.
Answers
Answer:
162
Step-by-step explanation:
V = LWH
L = 3
W = 6
H = 9
3 * 6 * 9 = 162
Jillian walked 0.5 miles before she started jogging at an average pace of 5 miles per hour. The equation d = 0.5 + 5t can be used to relate the total distance, d, in miles to the time, t, that Jillian spent jogging. What are the independent and dependent variables?
The independent variable is distance and the dependent variable is time.
The independent variable is time and the dependent variable is distance.
The independent variable is distance and the dependent variable is speed.
The independent variable is speed and the dependent variable is distance.
Answers
Answer:
The answer is option 2.
Step-by-step explanation:
In the question, the independent variable is time and dependent is distance. As the time changes, the distance will also change it means the distance depends on time.
For example,
[tex]d = 0.5 + 5t[/tex]
Let t = 1,
[tex]d = 0.5 + 5(1)[/tex]
[tex]d = 5.5 \: miles[/tex]
Let t = 5,
[tex]d = 0.5 + 5(5)[/tex]
[tex]d = 25.5 \: miles[/tex]
Therfore, as time increases, distance will also increase.
Answer:
B: The independent variable is time and the dependent variable is distance.
Step-by-step explanation:
edg2021
Given ΔMNO, find the measure of ∠MNO. A.28° B.38° C.52° D.76°
Answers
Answer:
The answer is 28! meaning A.If you need help understanding how I got the answer please let me know and I will gladly explain how I got the answer:)
I need help with question 3 so if you can take a little bit of your time to help that will be great :)
Answers
part B equals 1/2 and 1 hour
part C equals you just have to add all the times together where the dots are
Which expression is a sum of cubes?
-27a3b6+8a9b12
-9ab6 +9610
9ab6 + 8a12
27a3b8+8a9b12
Answers
Answer:
The first possible answer, -27a³b^6 + 8a^9b^12, is the sum of cubes.
Step-by-step explanation:
The middle two possible answers involve " a " with no exponent, so these could not be correct.
Looking at the first and fourth possible answers, we see that the first term of -27a3b6+8a9b12 is a perfect cube; it could be re-written as (-3ab²)³. The second term could be rewritten as (2a³b^4)³. So the first possible ansswer is the SUM of CUBES.
On a coordinate plane, a parallelogram has points A (negative 3, 4), B (3, 4), C (1, negative 2), and D (negative 5, negative 2). If a translation of (x, y) → (x + 6, y – 10) is applied to figure ABCD, what are the coordinates of D'? (–5, –2) (1, –12) (4, –15) (–9, –6)
Answers
Answer:
1,-12
Step-by-step explanation:
The coordinates of D' after translation is (1, -12).
Option B is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Parallelogram coordinates:
A = (-3, 4)
B = (3, 4)
C = (1, -2)
D = (-5, -2)
Now,
Translation of (x, y) → (x + 6, y - 10) is applied.
This means,
Parallelogram coordinates:
A' = (-3, 4) → (-3 + 6, 4 - 10) = (3, -6)
B' = (3, 4) → (3 + 6, 4 - 10) = (9, -4)
C' = (1, -2) → (1 + 6, -2 - 10) = (7, -12)
D' = (-5, -2) → (-5 + 6, -2 - 10) = (1, -12)
Thus,
The coordinates of D' is (1, -12).
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Which of the following equations describes the graph?
Answers
I would suggest using Desmos (a graphing website and app) to graph the equations and see which on fits the graph shown, in the future.
These dot plots show hourly earnings for a sample of workers in two
different careers.
Career A
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Career B
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Hourly eamings ($)
What are the differences between the centers and spreads of these
earning distributions?
Select two choices: one for the centers and one for the spreads.
O A. Centers: Career A has greater median hourly earnings
than career B.
B. Spreads: The hourly earnings for career B are more spread
out.
O c. Spreads: The hourly earnings for career A are more spread
out.
O D. Centers: Career B has greater median hourly earnings than
career A
Answers
Answer:
B and D
Step-by-step explanation:
The statement (A) Centres: Career A has greater median hourly earnings than career (B) and statement (B) Spreads: The hourly earnings for career B are more spread out are correct.
What is dot plot?A dot plot, also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
We have given dot plot in the picture.
As we can see from the dot plot:
Median for career A = 35
Median for career B = 25
And career B dot plot is more spread.
Thus, the statement (A) Centres: Career A has greater median hourly earnings than career (B) and statement (B) Spreads: The hourly earnings for career B are more spread out are correct.
Learn more about the dot plot here:
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Please help me with this. 5 star to the best.
Answers
Answer:
141.37 cm^3
Step-by-step explanation:
The volume of the hemisphere is 56.55 and the volume of the cone is 84.82. add them
Find the area of the trapezoid below.
4 cm
3cm
8 cm
Answers
24
I hope this is helpful
:)
Answer:
28
Step-by-step explanation:
base = ( a ) 4
base = ( b ) 3
height = ( h ) 8
A = a + b/2 x h = 4 + 3/2 x 8 = 28
If the sixth term in a geometric sequence is 1/625, and the common ratio is 15, find the explicit formula of the sequence.
A. an=(15)n−1 for n ≥ 1
B. an=(5)⋅(15)n−1 for n ≥ 2
C. an=(5)⋅(15)n−1 for n ≥ 1
D. an=(1)⋅(15)n−1 for n ≥ 2
Answers
Answer:
The explicit formula of the sequence is [tex]a_n=5(\frac{1}{5})^{n-1}[/tex] for [tex]n \geq 2[/tex]
Step-by-step explanation:
Sixth term in a geometric sequence =[tex]\frac{1}{625}[/tex]
Common ratio =[tex]\frac{1}{5}[/tex]
Formula of nth term =[tex]a_n=ar^{n-1}[/tex]
Substitute the values
So,[tex]\frac{1}{625}=a(\frac{1}{5})^{6-1}\\\frac{1}{625}=a(\frac{1}{5})^{5}\\\frac{1}{625} \times 5^5=a[/tex]
5=a
Substitute the value in 1
So,[tex]a_n=5(\frac{1}{5})^{n-1}[/tex]
So, Option C is true
Hence the explicit formula of the sequence is [tex]a_n=5(\frac{1}{5})^{n-1}[/tex] for [tex]n \geq 2[/tex]
Answer :)
C is the answer... so yea ★
Need some help
Take a look at the screenshot
The answer is not y= -1 + 9
Answers
Answer:
y = - x +9
Step-by-step explanation:
slope = (9-0)/(0-9) = - 1
line equation : y= mx + c
find c : 9= - 1*0 +c ....... >> c = 9
y = - x +9 ans
Answer:
y=-x+9Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(9-0)/((0-9))
m=9/(0-9)
m=9/-9
m=-1
y=mx+c
y=-1*x+c
y=-x+c
plug in (9,0) into the equation
0=-1*9+c
0=-9+c
-c=-9
c=9
y=-x+9
you wrote it correctly too, but I think the problem is that it only takes -x not -1x
If a = b, then xa = xb represents the property of equality. Question 6 options: A) multiplication B) symmetric C) addition D) reflexive
Answers
Answer:
A) multiplication
Explanation:
is a=b, then xa=xb, then the two are equal by the property of multiplication.
Answer:
Multiplication
Step-by-step explanation: I took the test
Sketch the graph of the given equation. y = x2 + 8x +15
Answers
What is the solution to this equation?
3(4x+6) = 9x + 12
O A. x= -2
B. X=-10
O c. x= 2
O D. x= 10
Answers
Answer:
I think it's A) x= - 2
Hope this helps..
The solution of the equation is,
⇒ x = - 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ 3 (4x + 6) = 9x + 12
Now,
Solve the equation as;
⇒ 3 (4x + 6) = 9x + 12
⇒ 12x + 18 = 9x + 12
⇒ 12x - 9x = 12 - 18
⇒ 3x = - 6
⇒ x = - 6/3
⇒ x = - 2
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Which of the following graphs shows b < 4 ?
Answers
Answer:
C
Step-by-step explanation:
< is an open circle and graph C is the only one with an open circle
Answer:
Choice C or the third one down
Step-by-step explanation:
b < 4
There is an open circle at 4 since there is no equals sign
and the lines goes to the left
Keith is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $120 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answers
Answer: m>50
Step-by-step explanation:
Hi, to answer this question we have to write an inequality:
The amount charged by company A (120) must be less (<) than the fixed amount charged by company B (75), plus the product of the cost per mile driven (0.90) and the number of miles driven (m).
120 < 75+ 0.90m
Solving for m:
120-75<0.90m
45<0.90m
45/0.90 <m
50<m
Company A charges less than Company B when m > 50.
Feel free to ask for more if needed or if you did not understand something.
PLEASE HELP I WILL MARK BRAINLIEST!
A storekeeper wishes to sell 100 pounds of mixed nuts for $1.75 a pound. He mixes peanuts worth $1.60 a pound with cashews worth $1.85 a pound. How many pounds of each does he use?
Answers
Answer:
40 pounds of nuts worth $1.60
60 pounds of nuts worth $1.85
Step-by-step explanation:
This is a mixture problem, so see the attachment below:
*Sorry if it's unclear, but I hope it helps!
which expression is equivalent to 3^4 x 3^x
Answers
Answer:
81, x⋅ 3x is your correct answer!
Solve the following equation by using the multiplicative inverse. MUST SHOW WORK
5/6x = - 10
Answers
Answer:
5/6x = -10
=> 5/6x = -10/1
by cross multiplication
=> 6x × - 10 = 5 × 1
=> 6x = 5 × 1 / -10
=> 6x = 1/-2
=> x = 1/-2 ×6
=> x = 1/-12
n is a positive integer
i) Explain why n(n+1) must be an even number?
ii) Explain why 2n-1 must be an odd number?
Answers
Answer:
Step-by-step explanation:
product of two consecutive numbers is always even.
n(n+1)
case 1
if n is odd,let n=2k+1,where k is an integer
n+1=2k+1+1=2k+2=2(k+1)
n(n+1)=(2k+1)[2(k+1)]=2(2k+1)(k+1)=even number.
case 2
if n is even,let n=2m,where m is an integer.
n+1=2m+1
n(n+1)=2m(2m+1)=even integer.
so in both cases n(n+1) is even.
Help asap plz, shhdhdhdhshdhdn
Answers
Answer:
x=30°
Step-by-step explanation:
Angles 4x and 2x are supplementary, so 4x+2x must be equal to 180°.
Therefore, to solve this problem, we must use the equation, "4x+2x=180°.
4x+2x=180
6x=180
x=30°
I hope this helps.
Find the circumference of the largest circle that can be inscribed inside a square whose side is 5" ( with explanation )
Answers
Answer:
22.21
Step-by-step explanation:
diagonal of square = 5 squareroot 2
diameter = 5 square root 2
circumfrence = 22.21
Simplify 7(x + 3). xxxxxxxxxxx
Answers
Answer:
[tex]7x+21[/tex]
Step-by-step explanation:
[tex]7(x + 3)[/tex]
[tex]7(x)+7(3)[/tex]
[tex]7x+21[/tex]
Answer:
7x + 21
Step-by-step explanation:
7 x X=7X
7 x 3=21
12
Find the area of the shaded reagion.
5 in
Answers
Plz help i will mark u brainiest
Answers
Answer:
Step-by-step explanation:
Well, first of all the shape needs to be a rectangle not a square. And i think you do not understand how coordinates work.
The coordinate (-1, 4). The first number -1 is the number on the x-axis, 4 is the number on the y-axis. Same thing with the other coordinate.
After you put down the two dots, you know that the Perimeter is 24 cm.
P = 2(a + b) = 24 => a+b = 12 => a = 4 => b = 8
The sides are 4 and 8 units long.
Hope this Helps))) ^‿^
Yuet solved the equation 6 a minus 2 b = 12 for a. Her steps are shown below. 1. Subtract 2b: 6 a = 12 minus 12 b 2. Divide by 6: a = 2 minus one-third b
Which statement about Yuet’s work is true?
In step 1 she needed to add 2b to both sides of the equation.
In step 1 she needed to divide by 2b on both sides of the equation.
In step 2 she needed to divide both sides of the equation by 6.
In step 2 she needed to subtract 6 from both sides of the equation.
Answers
Question:
Yuet solved the equation [tex]6a - 2b = 12[/tex] for a.
Her steps are shown below.
1. Subtract 2b: [tex]6a = 12 - 2b[/tex]
2. Divide by 6: [tex]a = 2 - \frac{b}{3}[/tex]
Answer:
In step 1 she needed to add 2b to both sides of the equation.
Step-by-step explanation:
Given:
The above steps shows how Yuet solved an equation
Required:
True statement about Yuet's work
The implication of the statement is to state what Yuet should have done instead of what she did.
In step 1, she subtracted 2b from both sides of the equation; this is wrong.
Instead of subtracting, she ought to add 2b to both sides of the equation.
The correct steps and result is as follows:
1. Add 2b: [tex]6a = 12 + 2b[/tex]
2. Divide by 6: [tex]a = 2 + \frac{b}{3}[/tex]
Hence, we can conclude that in step 1 she needed to add 2b to both sides of the equation.
Answer:
A:In step 1 she needed to add 2b to both sides of the equation.
Step-by-step explanation:
i did the test
The ordered pair below is a solution to which equation?
(40,5)
Answers
Answer: A
Step-by-step explanation:
Find the volume of the pyramid.
Answers
Answer:
V=5
12tan(54°)ha2=5
12·tan(54°)·4·152≈516.14322
Step-by-step explanation:
Thanks me later
Hope this helps!!!
