Given sec A= and that angle A is in Quadrant I, find the exact value of csc A in
simplest radical form using a rational denominator.
Need help :(
Answers
The required value is [tex]\csc A=\dfrac{5}{4}[/tex].
Important information:
[tex]\sec A=\dfrac{5}{3}[/tex]Angle A is in Quadrant I.We need to find the exact value of csc A.
Trigonometric Ratios:Formulae used: If angle A is in Quadrant I.
[tex]\cos A=\dfrac{1}{\sec A}[/tex]
[tex]\sin A=\sqrt{1-\cos^2 A}[/tex]
[tex]\csc A=\dfrac{1}{\sin A}[/tex]
Using these formulae, we get
[tex]\cos A=\dfrac{3}{5}[/tex]
And,
[tex]\sin A=\sqrt{1-\left(\dfrac{3}{5}\right)^2}[/tex]
[tex]\sin A=\sqrt{1-\dfrac{9}{25}}[/tex]
[tex]\sin A=\sqrt{\dfrac{16}{25}}[/tex]
[tex]\sin A=\dfrac{4}{5}[/tex]
Now,
[tex]\csc A=\dfrac{1}{\sin A}[/tex]
[tex]\csc A=\dfrac{1}{\frac{4}{5}}[/tex]
[tex]\csc A=\dfrac{5}{4}[/tex]
Thus, the required value is [tex]\csc A=\dfrac{5}{4}[/tex].
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The required value of cscA is 1.25
Given,
[tex]secA=\frac{5}{3}[/tex]
Trigonometrical ratios:
In the first quadrant, all ratios are positives.
[tex]sin A=\frac{P}{H}[/tex]
And the value of hypotenuse is,
[tex]P=\sqrt{H^2-B^2} \\=\sqrt{5^2-3^2} \\=\sqrt{16}\\ P=4[/tex]
So, the sine A is,
[tex]sinA=\frac{P}{H}\\ =\frac{4}{5}[/tex]
So, the rational denominator is,
[tex]cscA=\frac{H}{P}\\ =\frac{5}{4}\\=1.25[/tex]
Learn More about Trigonometrical ratios:
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solve the following inequality showing all steps -3n+7<4
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[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{-3n + 7 < 4}\\\\\textsf{SUBTRACT by 7 on your sides}\\\mathsf{-3n+7-7<4-7}\\\mathsf{Cancel\ out: 7-7\ because\ that\ gives\ you\ 0}\\\mathsf{Keep: 4-7\ because\ it\ helps\ us\ solve\ for\ our\ n \ value}\\\bf{{\mathsf{4-7= -3}}}\\\\\mathsf{New\ question: -3n<-3}\\\\\mathsf{DIVIDE\ both\ sides\ by\ -3}\\\mathsf{\dfrac{-3n}{-3}=\dfrac{-3}{-3}}\\\mathsf{Cancel\ out: \dfrac{-3}{-3} \ because\ gives\ us\ 1}\\\mathsf{Keep: \dfrac{-3}{-3}\ because\ it\ gives\ us\ our\ n\ value}[/tex]
[tex]\mathsf{New\ equation: n < \dfrac{-3}{-3}}\\\mathsf{\dfrac{-3}{-3} = -3\div-3 \rightarrow 1}\\\\\huge\textsf{Answer}\huge\downarrow\\\\\boxed{\boxed{\mathsf{Answer: n < 1}}}\checkmark\\\\\\\\\textsf{Good luck on your assignment and enjoy your day!}\\\\\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
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y = -5x + 54
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
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Answer:
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
Tye length of the ramp can be gotten using Pythagoras theorem.
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L =√109
L = 10.44ft
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Answer:
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Step-by-step explanation:
Answer:
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
Step-by-step explanation
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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1)
An ice machine uses 3 gallons of water every 9 hours. How many gallons of water does it use each hour? How many
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Answer:
B
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A)
b)
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He pays 18% income tax on everything he earns over $8200.
a Work out how much income tax he pays.
b Work out what percentage of his income he pays in tax.
If the income tax rate is increased to 21%, how much more tax will Sam pay?
Answers
Answer:
he would pay $8,293.5 in income tax.
b:
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Alaina is making a birdseed mix with 2 1/3 lb sunflower seeds, 5/6 lb cracked corn, and 1/6 lb peanuts. How much cracked corn does Alaina need to make 5 lb of birdseed mix? Show your work.
Answers
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Step-by-step explanation:
If you add everything it makes 3 and 1/3 pounds you want 5
If you divide 5 by 3 and 1/3 it's 1.5
Then you just need to multiply 5/6 by 1.5
For making 5 lb birdseed mix 1 ¹/₄ lb cracked corn will be used.
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A proportion is an equation based on the equality of two ratios.
Here it is given that :
Alaina is making a birdseed mix with 2 1/3 lb sunflower seeds, 5/6 lb cracked corn, and 1/6 lb peanuts.
adding everything to make birdseed mix = 2 1/3 + 5/6 + 1/6 =10/3 lb
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for making 10/3 lb birdseed mix = 5/6 lb cracked corn is used
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Answers
Answer:
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x = -15/4
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
-12, -3, 5, 9
Step-by-step explanation:
ok. So the numbers are 5, -3, -12, and 9.
In these numbers, there are 2 negatives. They are -12 and -3.
In negatives, the bigger the number is, the number is smaller.
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Suppose that P (A)=0.4 AND P (B)=0.2, If events A & B ARE Mutually EXCLUSIVE :
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- What is the probability of neither A nor B will happen
Answers
Part (a) Finding the probability of either A or B
We are told that events A and B are mutually exclusive. This means they cannot happen at the same time. We can say P(A and B) = 0
Furthermore,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.4 + 0.2 - 0
P(A or B) = 0.6
Answer: 0.6=======================================================
Part (b) Finding the probability of neither A nor B
P(A or B) + P(neither A nor B) = 1
P(neither A nor B) = 1 - P(A or B)
P(neither A nor B) = 1 - 0.6
P(neither A nor B) = 0.4
The reason why this works is to imagine throwing a dart at the Venn diagram. You'll either...
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Answer: 0.4Three friends are selling items at an arts and crafts fair. Kim makes $45.75 selling jewelry. Mark makes 100 times as much as Kim selling his custom picture frames. Carlos makes one tenth of the money Mark makes selling paintings. How much money does each friend make?
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Answer:
mark is making $4,575, Carlos is makeing 457.50
Mrs. Healy has two dogs rocky and chino. rocky eats 2 dog treats each day and Chino eats 5 each day. How many treats do the dogs eat in 4 days?
Answers
Answer:
28 treats
Step-by-step explanation:
2x4
5x4
20+8=28
Answer:
the answer is 28 treats in 4 days for both dogs
Step-by-step explanation:
2*4=8+ 5*4=20= all together 28 treats for 2 dogs
hope this helped