if cot 17 degrees = 3.2709, find tan 73 degrees
To find tan 73 degrees, we can use the relationship between cotangent and tangent.
Recall that cotangent (cot) is the reciprocal of tangent (tan), meaning that if cot 17 degrees = 3.2709, then tan 17 degrees = 1/cot 17 degrees.
Let's find tan 17 degrees first:
1. Calculate the reciprocal of cot 17 degrees.
Reciprocal of 3.2709 = 1/3.2709 ≈ 0.30529
Now that we have tan 17 degrees, we can use the following trigonometric identity to find tan 73 degrees:
tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
Let A = 17 degrees and B = 56 degrees (73 degrees - 17 degrees).
tan 73 degrees = tan (17 degrees + 56 degrees)
Using the identity:
tan (17 degrees + 56 degrees) = (tan 17 degrees + tan 56 degrees) / (1 - tan 17 degrees * tan 56 degrees)
Now we need to calculate tan 56 degrees.
Since we already have tan 17 degrees, we can calculate tan 56 degrees using the following trigonometric identity:
tan(A - B) = (tan A - tan B) / (1 + tan A * tan B)
Let A = 56 degrees and B = 17 degrees (56 degrees - 17 degrees).
tan (56 degrees - 17 degrees) = (tan 56 degrees - tan 17 degrees) / (1 + tan 56 degrees * tan 17 degrees)
After calculating tan 56 degrees using this identity, substitute the values into the previous equation:
tan (17 degrees + 56 degrees) = (tan 17 degrees + tan 56 degrees) / (1 - tan 17 degrees * tan 56 degrees)
Finally, substitute the value of tan 17 degrees (0.30529) into the equation:
tan 73 degrees ≈ (0.30529 + tan 56 degrees) / (1 - 0.30529 * tan 56 degrees)
Solving this equation will give you the value of tan 73 degrees.
There are 3 co-ratios
sine vs cosine
secant vs cosecant
tangent vs cotangent
that is, sin(x) = cos(90°-x)
so cot(17°) = tan(90-17) = tan 73° = 3.2709