Will give brainliest to anyone who answers correctly btw the lines on top stand for the dots .
1 answer:
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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
The question can be rewritten to
This case about equations with one variable. We have to solve this calculation to obtain the value of M. Our task is to isolate the variable M alone at the end of the process on one side of the equation until the variable will be equal to a value on the opposing side.
Let's arrange it into an equation, i.e.,
Turn this equation over so that the position of variable M is on the left side.
Both sides are multiplied by 10 to isolate M on the left side. The fraction are eliminated.
M = 1,000
Therefore, we have calculated the number that was asked.
Hence
<u>Note: </u>
The significant thing to carry out is how to manipulate both sides of the equation with the algebraic properties of equality such as:
- Adding
- Subtracting
- Multiplying, and/or
- Dividing both sides of the equation with a similar number
And the commutative property of multiplication, i.e.,
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Keywords: 100 is 1/10 of, solve, 1,000, variable, 2/7m - 1/7 = 3/14, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, equal, the opposite, both sides are multiplied by, turn, calculation
