How would you solve tan(-335) without using a calculator? I got it to tan(25) but that's not one of the ones on our chart, and I'd use a sum or difference identity but we never learned one for tangent, if one exists.
I don't see a solution without a calculator.
Assuming the angles are in degrees,
tan (-335) = -tan 25
Use tan (a + b) = (tana + tanb)/[1 - (tana*tanb)]
I don't see a suitable combination of a and b, either.
To solve for tan(-335) without using a calculator, we can make use of the periodicity and symmetry properties of the tangent function.
First, let's determine the equivalent angle within one full revolution (360 degrees) that is congruent to -335 degrees. Since -335 degrees is negative, we can add 360 degrees to it until we obtain a positive equivalent angle:
-335 + 360 = 25 degrees
Now, we have an angle of 25 degrees for which we can find the tangent value. However, as you mentioned, there is no specific value provided for tangent(25) on your chart. In this case, we can use the sum or difference identity for tangent, which states:
tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
Since we don't have a specific identity for tangent, we can use the fact that tangent is equal to the ratio of sine over cosine:
tan A = sin A / cos A
Using this, we can rewrite the tangent identity as:
tan(A + B) = (sin A / cos A + sin B / cos B) / (1 - (sin A / cos A) * (sin B / cos B))
Now, let's apply this identity to find a value for tangent(25) using any other tangents that are on your chart. For example, if you have tangent(10) and tangent(15) on your chart, you can express tangent(25) as:
tan(10 + 15) = (tan 10 + tan 15) / (1 - tan 10 * tan 15)
Using the values from your chart, substitute the known tangent values and compute the result. This will help you find an approximation for tangent(25) without using a calculator.