Fine the measure of feta, to nearest degree, where 0 degrees is less or equal to feta, and feta is less or equal to 360 degrees.
tan feta + 5 = 0, I tried working this out and I got -78.6:\
There is that Greek cheese feta again.
tanØ = -5
the tangent is negative in II and IV
angle in standard position is 78.69°
Ø = 360-78.69 = 281.13 in IV
Ø = 180 - 78.69 = 101.13° in II
check by taking the tangent of each of those
Help Me...?
xD
To solve the equation tan(feta) + 5 = 0, we need to isolate feta. Let's go step by step:
1. Start with the equation: tan(feta) + 5 = 0
2. Subtract 5 from both sides: tan(feta) = -5
3. Take the inverse tangent (arctan or tan^(-1)) of both sides to isolate feta: feta = arctan(-5)
Now, let's find the value of arctan(-5).
Note: The arctan function gives values in radians. If you need the answer in degrees, we can convert it afterward.
Using a calculator, arctan(-5) ≈ -78.69 radians.
To convert radians to degrees, we can use the conversion factor that 180 degrees equals π radians:
feta ≈ -78.69 * (180/π) ≈ -4499.84 degrees
However, since we need the value of feta between 0 and 360 degrees, we need to find an equivalent measurement within that range. We can do this by adding or subtracting multiples of 360 degrees until we're within the desired range.
Since -4499.84 is negative, we know that every addition of 360 degrees will bring us closer to 0. Let's add 360 degrees multiple times until we get a positive value:
-4499.84 + 360 = -4139.84 (still negative)
-4139.84 + 360 = -3779.84 (still negative)
-3779.84 + 360 = -3419.84 (still negative)
-3419.84 + 360 = -3059.84 (still negative)
-3059.84 + 360 = -2699.84 (still negative)
-2699.84 + 360 = -2339.84 (still negative)
-2339.84 + 360 = -1979.84 (still negative)
-1979.84 + 360 = -1619.84 (still negative)
-1619.84 + 360 = -1259.84 (still negative)
-1259.84 + 360 = -899.84 (still negative)
-899.84 + 360 = -539.84 (still negative)
-539.84 + 360 = -179.84 (still negative)
-179.84 + 360 = 180.16 (within the range)
Therefore, the solution within the given range is feta ≈ 180 degrees (to the nearest degree).
To find the measure of feta, we can use the inverse of the tangent function (known as arctan or atan) to solve the equation. Let's start step by step:
1. Begin with the equation: tan(feta) + 5 = 0
2. Subtract 5 from both sides to isolate the tangent term: tan(feta) = -5
3. Now, take the arctan (inverse tangent) of both sides to find the measure of feta: feta = arctan(-5)
4. Plug the equation into a calculator or use a trigonometric table to find the arctan(-5) value.
Note: The tangent function repeats every 180 degrees, so we can add or subtract multiples of 180 to the arctan(-5) value to find all possible solutions.
Using a calculator, we find that arctan(-5) is approximately -78.69 degrees. Since feta is within the range of 0 to 360 degrees, we add 180 degrees to get the equivalent angle in the positive range:
-78.69° + 180° = 101.31°
Therefore, the measure of feta, rounded to the nearest degree, is 101 degrees.