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3 years ago

Find the value of each expression using the given information cot∅=8, csc<0 find sin ∅

Mathematics

1 answer:

Oksana_A [137]3 years ago

6 0

9514 1404 393

Answer:

sin(∅) = -√65/65

Step-by-step explanation:

The identities that relate the cotangent, the cosecant, and the sine are ...

csc² = 1 +cot²

sin = 1/csc

_____

For the given values, we find ...

csc(∅)² = 1 +cot(∅)² = 1 +8² = 65

csc(∅) = -√65 . . . . . . . . . . . . . . . . square root with attention to sign

sin(∅) = -1/√65 = (-√65)/65

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mote1985 [20]

<h2>Answer with explanation:</h2>

Given : In a restaurant, the proportion of people who order coffee with their dinner is p.

Sample size : n= 144

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The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-

Null hypothesis : $H_0: p\geq0.85$ [ it takes equality (=, ≤, ≥) ]

Alternative hypothesis : $H_1: p$ [its exactly opposite of null hypothesis]

∵Alternative hypothesis is left tailed, so the test is a left tailed test.

Test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$z=\dfrac{0.83-0.85}{\sqrt{\dfrac{0.85(1-0.85)}{144}}}\\\\=-0.561232257678\approx-0.56$

Using z-vale table ,

Critical value for 0.05 significance ( left-tailed test)=-1.645

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