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ratelena [41]
3 years ago
11

Please solve 5 f (Trigonometric Equations) #salute u if u solved it

Mathematics
1 answer:
Zanzabum3 years ago
4 0

Answer:

\beta=45\degree\:\:or\:\:\beta=135\degree

Step-by-step explanation:

We want to solve \tan \beta \sec \beta=\sqrt{2}, where 0\le \beta \le360\degree.

We rewrite in terms of sine and cosine.

\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}

\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}

Use the Pythagorean identity: \cos^2\beta=1-\sin^2\beta.

\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}

\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)

\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta

\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0

This is a quadratic equation in \sin \beta.

By the quadratic formula, we have:

\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }

\sin \beta=\frac{2}{2\cdot \sqrt{2} } or \sin \beta=\frac{-4}{2\cdot \sqrt{2} }

\sin \beta=\frac{1}{\sqrt{2} } or \sin \beta=-\frac{2}{\sqrt{2} }

\sin \beta=\frac{\sqrt{2}}{2} or \sin \beta=-\sqrt{2}

When \sin \beta=\frac{\sqrt{2}}{2} , \beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )

\implies \beta=45\degree\:\:or\:\:\beta=135\degree on the interval 0\le \beta \le360\degree.

When  \sin \beta=-\sqrt{2}, \beta is not defined because -1\le \sin \beta \le1

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0

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What is the mean of -9,-5,-4,-4,-2,0,1,2,3,5
IrinaK [193]

Answer: - 1.3

Step-by-step explanation: I believe that it's -1.3 if you're referring to the arithmetic mean.

(1) Take the sum of -9, -5, -4, -4, -2, 0, 1, 2, 3, 5 and simplify it to -13

(2) Count the number of terms in the data set.

{-9, -5, -4, -4, -2, 0, 1, 2, 3, 5}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - The number of terms in the data set is <u>10.</u>  

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8 0
3 years ago
Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre
Sergeu [11.5K]

Answer: No, Cammie is not correct. She can mow  1\frac{1}{5}\ acres in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow \frac{1}{2}\ acre in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

\frac{\frac{1}{2}}{25}=\frac{x}{60}

Solving for "x", you get:

\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

x=1\frac{1}{5}

Therefore, she can mow  1\frac{1}{5}\ acres in one hour.

3 0
3 years ago
MATH HELP...PLz
PilotLPTM [1.2K]

a. 14, 18, 22, 26.... It is +4

b. 2,430, 7,290, 21,870..... It is x3

c. So it is going -2, -4, -6, -8 so the next one would be -10 which is -13 then -12 which is -25 and so on.

Hope this helps!


8 0
3 years ago
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