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.