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Find all angles in degrees that satisfy the equation Round approximate answers to the nearest tenth of a degree tan a -1.64 O = a O = a = 31,4° + k180° O = a = 121,4° + k180° O = a = 238,6° + k180°

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Answer:

a≈−59.46∘a≈−59.46∘ (from the first equation)

a=148.6∘+k⋅180∘a=148.6∘+k⋅180∘ (from equations 2, 3, 4, and 5)

Explanation:

It looks like you have equations involving the tangent function, and you want to find angles (a) that satisfy these equations. The general form of these equations is:

tan⁡(a)=−1.64tan(a)=−1.64

Let's start with the first equation:

tan⁡(a)=−1.64tan(a)=−1.64

To find the values of aa that satisfy this equation, you can use the inverse tangent function (often denoted as tan⁡−1tan−1 or \text{arctan}). Taking the arctan of both sides:

a=tan⁡−1(−1.64)a=tan−1(−1.64)

Using a calculator, you can find the approximate value of aa:

a≈−59.46∘a≈−59.46∘ (rounded to one decimal place)

Now, you have a≈−59.46∘a≈−59.46∘ as a solution to the first equation.

Next, it seems you have several equations with a similar form:

a=148.6∘+k180∘a=148.6∘+k180∘ (where kk is an integer)

a=31.4∘+k180∘a=31.4∘+k180∘

a=121.4∘+k180∘a=121.4∘+k180∘

a=238.6∘+k180∘a=238.6∘+k180∘

These equations represent angles in different quadrants, and adding k⋅180∘k⋅180∘ allows for multiple solutions. To find all solutions, you can substitute different integer values for kk and solve for aa.

For example, using equation (2) with k=0k=0, you get a=148.6∘a=148.6∘. With k=1k=1, you get a=148.6∘+180∘=328.6∘a=148.6∘+180∘=328.6∘, and so on. You can do a similar process for the other equations.

In summary, the solutions for aa are:

a≈−59.46∘a≈−59.46∘ (from the first equation)

a=148.6∘+k⋅180∘a=148.6∘+k⋅180∘ (from equations 2, 3, 4, and 5)

Where kk can be any integer, and aa is in degrees.

User Johnbaltis
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