Answer:
- make sure calculator is in "radians" mode
- use the cos⁻¹ function to find cos⁻¹(.23) ≈ 1.338718644
Step-by-step explanation:
A screenshot of a calculator shows the cos⁻¹ function (also called arccosine). It is often a "2nd" function on the cosine key. To get the answer in radians, the calculator must be in radians mode. Different calculators have different methods of setting that mode. For some, it is the default, as in the calculator accessed from a Google search box (2nd attachment).
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The third attachment shows a graph of the cosine function (red) and the value 0.23 (dashed red horizontal line). Everywhere that line intersects the cosine function is a value of A such that cos A = 0.23. There are an infinite number of them. You need to know about the symmetry and periodicity of the cosine function to find them all, given that one of them is A ≈ 1.339.
The solution in the 4th quadrant is at 2π-1.339, and additional solutions are at these values plus 2kπ, for any integer k.
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Also in the third attachment is a graph of the inverse of the cosine function (purple). The dashed purple vertical line is at x=0.23, so its intersection point with the inverse function is at 1.339, the angle at which cos(x)=0.23. The dashed orange graph shows the inverse of the cosine function, but to make it be single-valued (thus, a <em>function</em>), the arccosine function is restricted to the range 0 ≤ y ≤ π (purple).
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So, the easiest way to answer the problem is to use the inverse cosine function (cos⁻¹) of your scientific or graphing calculator. (<em>Always make sure</em> the angle mode, degrees or radians, is appropriate to the solution you want.) Be aware that the cosine function is periodic, so there is not just one answer unless the range is restricted.
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I keep myself "unconfused" by reading <em>cos⁻¹</em> as <em>the angle whose cosine is</em>. As with any inverse functions, the relationship with the original function is ...
cos⁻¹(cos A) = A
cos(cos⁻¹ a) = a
By=x+2, as this is the only equation that shows the relation between 2 variables
Answer:
1/4 of the times
Step-by-step explanation:
because there are 4 sections, that means that there is a 1/4 probability.
Answer: 54 students in each bus
Step-by-step explanation:
331 - 7 = 324
324 ÷ 6 = 54.
There were 54 students in each bus.
Answer:
No there cannot be.
Step-by-step explanation:
In explaining this question, I would like us to take into account who the barber is,
" the barber is the one who shaves all those, and those only, who do not shave themselves".
This barber cannot be in existence because who would shave him? If he should shave himself then there is a violation of the rule which says he shaves only those who do not shave themselves. If he shaves himself then he ceases to be a barber. And if he does not shave himself then he happens to be under those who must be shaved by the barber, because of what the rule says. But then he is the barber.
This lead us to a contradiction.
Neither is possible so there is no such barber.