Answers
Since both cot(θ) and cos(θ) are positive, it follows that sin(θ) is also positive:
cot(θ) = cos(θ)/sin(θ) > 0 ===> sin(θ) > 0
Recall the Pythagorean identity:
sin²(θ) + cos²(θ) = 1
Multiplying both sides by 1/sin²(θ) yields another form of the identity,
sin²(θ)/sin²(θ) + cos²(θ)/sin²(θ) = 1/sin²(θ)
1 + cot²(θ) = csc²(θ)
so that
csc(θ) = + √(1 + cot²(θ))
csc(θ) = √(1 + (3/2)²)
csc(θ) = √13/2
By definition of cosecant, we have
csc(θ) = 1/sin(θ)
so that
sin(θ) = 2/√13
Then using the Pythagorean identity once more, we have
cos(θ) = + √(1 - sin²(θ))
cos(θ) = √(1 - (2/√13)²)
cos(θ) = 3/√13
so that, by definition of secant,
sec(θ) = 1/cos(θ)
sec(θ) = √13/3
Related Questions
Identify the domain
of the following function.
PLS HELP
Answers
A politician has $4,200 to buy TV advertisements. If each advertisement costs $700, how many advertisements can the politician buy?
Answers
they can buy 6 tv advertisements.
Which exponential equation is equivalent to this logarithmic equation?
log x 5+ log x 12 = 7
Answers
Answer:
[tex]{ \rm{ log_{x}(5) + log_{x}(12) = 7}} \\ \\ { \rm{ log_{x}(5 + 12) = 7}} \\ \\ { \rm{ log_{x}(17) = 7}} \\ \\ { \rm{17 = {x}^{7} }} \\ \\ { \boxed{ \rm{ {x}^{7} = 17 }}}[/tex]
• further more:
[tex]{ \rm{x = \sqrt[7]{17} }} \\ \\ { \boxed{ \rm{x = 1.5}}}[/tex]
The equivalent exponential equation is given by [tex]x^7 - 60 = 0[/tex].
What is an equation?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
As per the given data:
We are given a logarithmic equation, and we have to find out the equivalent equation with exponents.
The logarithmic equation given in the question is:
[tex]log_x5 + log_x12 = 7[/tex] ...(i)
By using the following property of logarithm, we can simplify this equation.
[tex]log_x(ab) = log_xa + log_xb[/tex]
By using this property in eq (i)
[tex]log_x[5 \times 12] = 7[/tex]
[tex]log_x[60] = 7[/tex]
By using logarithmic transformation.
[tex]x^7 = 60[/tex]
∴ [tex]x^7 - 60 = 0[/tex]
The equivalent exponential equation is given by [tex]x^7 - 60 = 0[/tex].
Hence, The equivalent exponential equation is given by [tex]x^7 - 60 = 0[/tex].
To learn more about equation, click:
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Cecilia owns just as many cats as she does birds. If her pets have a total of 18 legs, how many cats does she own?
Answers
Answer:
1
Step-by-step explanation:
You can get this answer by adding 4+4+4+4, equaling out to 16...but how is there 18? well you just add 2 for the bird's legs and that's your answer!!
Hope this helps you love!!!
Answer:
3
Step-by-step explanation:
3 cats with 4 legs = 12
3 birds with 2 legs =6
12 + 6=18
i rlly need help--plzzzzzzzzzzzzzzzzz 10 points
Answers
Answer:
Harper is 200 yards away from her home if the map shows 3 inches
Step-by-step explanation:
50 yards = 3/4 inch
3 inches = 3/1
3/1 x 4/4 = 12/4
12/4 = 3 inches
50 x 4 = 200
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
A. 23.7
B. 8.7
C. 13.8
D. 9.5
Answers
Answer:
a
Step-by-step explanation:
just cuzyfhyf
Thomas, a waiter at a local restaurant, is paid $ 4 an hour plus tips. His friend Marie works at a local bookstore for $12 an hour. Marie and Thomas worked the same number of hours. If Thomas made $120 in tips and both made the same amount of money, how many hours
1.please just give me the first step on how it’s written out
Answers
Answer:
15 hours
Step-by-step explanation:
Let h = numbers of hour worked, x = tips, t = Thomas' pay, and m = Marie's pay
We can set up an equation for this question:
t = 4h + x
Now plug in 120 for x
t = 4h + 120
Now we set up Marie's pay:
m = 12h
Since Thomas and Marie made the same amount of money over the same number of hours, we can say:
4h + 120 = 12h
120 = 8h
h = 15
This means they both worked for 15 hours.
what multiplies to get 27 but adds to get -1
Answers
Answer:
9×3
and
-26
Step-by-step explanation:
9×3=27
27+-26
If u(x) = x^5-x^4x+x^2 and v(x)=-x^2, which expression is equivalent to (u/v)(x)?
Answers
Step-by-step explanation:
(x^5/-x^2)-(x^4x/-x^2)+(x^2/-x^2)
-x^3+x^2-1
Use the vertical line test to determine whether the relation graphed below is a function.
A. Yes
B. No
C. It cannot be determined.
Answers
Answer:
No
Step-by-step explanation:
Draw a vertical line. If a vertical line passes through two or more points on the graph, it is not a function. Since it passes through 2 points, it is not a function
pls help me this is due tonight by 8 40
Answers
Answer:
a. gh³
b. xy³
Step-by-step explanation:
a. [tex]g^{3-2}[/tex][tex]h^{5-2}[/tex] = gh³
b. [tex]x^{3-2} y^{4-1} p^{1-1}[/tex] = xy³
Use the negative exponent rule.
You buy a new computer for $1.500. The value of the computer decreases by 6% every yearHow much is the computer worth after 4 years?
a. $1,171.05
b. $1,225.35
c. $1,008.50
d. $999.80
Answers
Answer:
A. $1171.05Step-by-step explanation:
1500 × (1-(6 / 100))⁴
Hope this helped. A brainliest would be very much appreciated. (I need 4 brainliest so I can level up) :)
Answer:
b. $1,225.35
Step-by-step explanation:
HEEEEEEEEEEEEEEEELP MEEEEEEEEEEEEEEEEEEEEEE
Answers
answer: the inequality is 3+7(x)<24
x=x < 3 2/7
Step-by-step explanation:
because...
3 + 7x < 26
7x < 23
x < 23/7
x < 3 2/7
Answer:
More/Product is a key word to multiply so 3X7 and less is a key word to subtract so your subtracting X from 24
3x7=21 and that's 3 less than 24
The answer is 3
Step-by-step explanation:
The graph of linear function fpasses through the point (1, -9) and has a slope of 3.
What is the zero of f?
4
-2
2
-6
Will give brainliest if your right
Answers
Slope=-3
Coordinates= (1,-9)
Two cars leave San Francisco at the same time traveling in opposite directions. One travels at an
average speed of 74 mph and the other at 78 mph. In how many hours will they be 304 miles apart?
Let x = time of travel for the first car and y = time of travel for the second car.
Then the system that
models the problem is {74x + 78y=304}
Solve the system by using the method of addition.
Answers
Answer:
i don't really know but can you explain more so I can understand how to do it
need an answer, please need an answer, please
Answers
Answer:
Step-by-step explanation:
1) 6 and -5
x₁ + x₂ = 6 +(-5) = 1
x₁* x₂ = 6*(-5) = -30
x² -(x₁ + x₂)x + (x₁* x₂)=0
x² - x - 30 = 0
2) 4 and 7
x₁ + x₂ =4 + 7 = 11
x₁* x₂ = 4*7 = 28
x² - 11x + 28 = 0
3) 1 and -10
x₁ + x₂ = 1 +(-10) = -9
x₁* x₂ = 1*(-10) = -10
x² - 9x - 10 = 0
4) -9 and 0
x₁ + x₂ = -9 + 0 = -9
x₁* x₂ = 0
x² - (-9)x = 0
x² + 9x = 0
5)2 and 6
x₁ + x₂ = 2 + 6 = 8
x₁* x₂ = 2*6 = 12
x² -8x + 12 = 0
8) 2 +√3 and 2 - √3
x₁ + x₂ = 2+ √3 + 2 - √3 = 4
x₁* x₂ = (2 + √3)(2 - √3) = 2² - (√3)² 4 - 3 = 1
x² - 4x + 1 = 0
What is 3763.2 ÷0.512 with the work that goes with it.
Answers
Answer:
7350
Explanation:
3763.2/0.512 can be determined by simply dividing.
Simplify, the solve.
Answers
Answer:
1/64
Step-by-step explanation:
4x4^3/4^7
4^-3
1/4^3
1/64
find the other endpoint of the line segment with the given endpoint and midpoint.
endpoint- (-6,4) and midpoint (4,8)
Answers
Answer:
(14,12)
Step-by-step explanation:
Answer:
(14,12)
Step-by-step explanation:
(4,8)
(-6,4)
find the coordinates of the unknown endpoint
(14,12)
The diameter of a circle has length 12. The center is at (-5,2) . Give the equation of the circle?
Answers
9514 1404 393
Answer:
(x +5)² +(y -2)² = 36
Step-by-step explanation:
The radius is half the diameter, so is 12/2 = 6.
The standard form equation for a circle is ...
(x -h)² +(y -k)² = r² . . . . . . circle centered at (h, k) with radius r
For the given parameters, the equation is ...
(x +5)² +(y -2)² = 36
What is the value of the expression shown below? (4 points) 2 over 3 to the power of 2 + 5 × 2 − 4
Answers
Answer:
6 4/9Step-by-step explanation:
2 over 3 to the power of 2 + 5 × 2 − 4
[tex](2/3)^2+5*2-4=[/tex][tex]4/9 + 10-4=[/tex][tex]4/9+6=[/tex]6 4/9(2/3)^2 +5×2−4
=4/9 + 10-4
=4/9+10−4
=4/9+6
= [tex]6 \frac{4}{9} [/tex]
Therefore, 6 4/9 is ur answer
Which of the following graphs represents a function? Choose all that apply.
Answers
What is the image point of (9, -1) after the transformation T-4,-3 0 R270°?
Answers
Answer:
Given A point (9,-1) is first translated by rule T-4,3 : ( x,y ) goes ( x - 4 , y+ 3) followed by rotation of 270°
rule of rotation of 270° : ( x , y ) goes ( y,-x )
image of ( 9 , -1) after translation :
( 9 - 1) goes (-9,-1+3)=(-9,2)
then , image after rotation of 270° :
( -9,2 ) goes (2,9 p
hence , the image point of ( 9,-1 ) (9,-1)
after the transformation T-4,3 and rotation of 270°i is ( 2,9 ).
Step-by-step explanation:
hope it helps
8. Elijah has $2800.00. He gets a check for $300.00. He takes his mom out for dinner that costs $150.00. He finds$200.00 on Utopian Street, he then pays his friend Christian back $175, finally he pays his car insurance for $115.How much money does he have left?__________
Answers
Answer:
$2060
Step-by-step explanation:
2800+300-150-175-115= $2060
Answer:
2860
Step-by-step explanation:
2800+300-150+200-175-115=2860
Determine whether the ordered pair (6,5) is a solution to the equation -2x +y = -7.
O Yes, (6,5) is a solution.
O No.(6,5) is not a solution.
Answers
Answer:
yes (6,5) is a solution
Step-by-step explanation:
1
_ x + 9 for x=3 .............................................
2
Answers
Answer:
10.5
Step-by-step explanation:
[tex] \frac{1}{2} \times 3 + 9 \\ 1.5 + 9 \\ 10.5[/tex]
[tex]\\ \tt\Rrightarrow 1/2x+9[/tex]
x=3[tex]\\ \tt\Rrightarrow x/2+9[/tex]
[tex]\\ \tt\Rrightarrow 3/2+9[/tex]
[tex]\\ \tt\Rrightarrow 3+18/2[/tex]
[tex]\\ \tt\Rrightarrow 21/2[/tex]
[tex]\\ \tt\Rrightarrow 10.5[/tex]
If 7 4/5 is added to 2 3/4 , what is the sum?
Answers
Answer: 9 7/20
Step-by-step explanation:
7 4/5 + 2 3/4
Multiply the Denominators = 20
Add Numerators = 7
Add Whole Numbers = 9
Answer 9 7/20
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
ydkyksykdysjgjzgjz
Step-by-step explanation:
hlxkzgkzgksykkxmhxykdkydxkhoueydozgkhmzmhxkhdyoeoyxydkydkmxhylekdhkkysykyskkkysyek sheets obvi redfin
This table shows the relationship between time and push-ups.
Which of the following values could represent the value of r2 for this relationship?
r2 = ‒0.9646
r2 = ‒0.0354
r2 = 0.0354
r2 = 0.9646
Answers
Answer:
D
Step-by-step explanation: i <3 satistics so much
ABC, Construct a triangle ABC, <B =90° AB= 4cm AC=5cm. Find the third side.
Helpppp
Answers
Pythagoras Theorem
BC = 3 cm
Step by step explanation :
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