Problem 89 - Algebra and Trigonometry

Question

Use words to describe the formula for: the tangent of half an angle. (Describe one of the two formulas that does not involve a square root.)

Step-by-Step Solution

Answer

The tangent of half the angle equals the difference of one and the cosine of the angle divided by the sine of that same angle.

Step 1: Identify the formula

First, locate the formula that doesn't involve a square root. In our case, we can use the following tangent of half-angle formula: \[ \text{tan}(\frac{θ}{2})=\frac{1-\text{cos}(θ)}{\text{sin}(θ)} \]

Step 2: Describe the formula in words

Describe the formula in plain English. For instance, it can be interpreted as: The tangent of half the angle equals the difference of one and the cosine of the angle divided by the sine of that same angle.

Step 3: Conclusion statement

In summary, we have described the tangent half-angle formula in words, specifically one that does not require the use of a square root.