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2 years ago

How are the expressions 0.4+1.5 and 1.5 +0.4 alike? different?

Mathematics

2 answers:

viktelen [127]2 years ago

7 0

They’re equal but have different forms

pav-90 [236]2 years ago

5 0

They are equal to each other

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Dimas [21]

Answer:

$csc(\theta)=\frac{5}{3}$

Step-by-step explanation:

If the $tan(\theta)=\frac{3}{4}$ , then the cotangent is $\frac{4}{3}$ , given that:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$ , and $cot(\theta)=\frac{cos(\theta)}{sin(\theta)}$ .

This is important to know because if you recall the three Pythagorean identities in trigonometry, one of them involves a nice relationship between the cotangent and the cosecant of an angle:

$1+cot^2(\theta)=csc^2(\theta)$

so we can replace $cot(\theta)$ with 4/3, and find what $csc(\theta)$ is using that identity:

$1+cot^2(\theta)=csc^2(\theta)\\1+(\frac{4}{3})^2= csc^2(\theta)\\1+\frac{16}{9} =csc^2(\theta)\\\frac{25}{9} = csc^2(\theta)\\csc(\theta)=+/-\sqrt{\frac{25}{9}} \\csc(\theta)=+/-\frac{5}{3}$

Now, you have to decide on which sign to use. So consider that if the tangent was positive, so most likely you are dealing with an angle $\theta$ between 0 and $\frac{\pi }{2}$ , and in that quadrant, the cosecant is positive.

Therefore, pick the positive value: 5/3

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