Questions: If θ = 9π/4, then sin(θ) equals 0.7071 cos(θ) equals 0.7071 tan(θ) equals 1 sec(θ) equals □

Transcript text: If $\theta=\frac{9 \pi}{4}$, then $\sin (\theta)$ equals 0.7071 $\cos (\theta)$ equals 0.7071 $\tan (\theta)$ equals 1 $\sec (\theta)$ equals $\square$

Solution

Solution Steps

To find $\sec(\theta)$, we need to use the identity $\sec(\theta) = \frac{1}{\cos(\theta)}$. Given that $\cos(\theta) = 0.7071$, we can calculate $\sec(\theta)$ by taking the reciprocal of $\cos(\theta)$.

Step 1: Given Values

We are given that $ \cos(\theta) = 0.7071 $.

Step 2: Calculate $ \sec(\theta) $

Using the identity $ \sec(\theta) = \frac{1}{\cos(\theta)} $, we can substitute the given value: \[ \sec(\theta) = \frac{1}{0.7071} \]

Step 3: Compute the Value

Calculating the reciprocal gives: \[ \sec(\theta) \approx 1.4142 \]