Problem 120 - Precalculus with Limits

Question

In Exercises \(119-122,\) use a calculator to demonstrate the identity for each value of \(\theta\). \(\tan ^{2} \theta+1=\sec ^{2} \theta\) (a) \(\theta=346^{\circ} \quad\) (b) \(\theta=3.1\)

Step-by-Step Solution

Answer

Upon computing the values on each side of the equation for both values of \( \theta \), one should find that \( \tan^2 \theta + 1 \) equals \( \sec^2 \theta \) for both \( \theta = 346^\circ \) and \( \theta = 3.1 \) demonstrating the validity of the given identity.

Step 1: Verify Identity for \( \theta = 346^\circ \)

Convert degrees to radians by multiplying the degree measurement by \( \frac{\pi}{180} \). So, \( 346^\circ = 346 \cdot \frac{\pi}{180} \) radians. Compute \( \tan^2(346^\circ) \) and \(\sec^2(346^\circ) \). If the identity holds true, these two values should be equal.

Step 2: Verify Identity for \( \theta = 3.1 \)

In this case, \( \theta \) is given in radians. Compute \( \tan^2(3.1) \) and \( \sec^2(3.1) \). Again, these two values should be equal if the identity holds true.