Questions: If θ=7π/6, then find exact values for the following: sec (θ) equals □ csc (θ) equals □ tan (θ) equals □ cot (θ) equals □

Transcript text: If $\theta=\frac{7 \pi}{6}$, then find exact values for the following: $\sec (\theta)$ equals $\square$ $\csc (\theta)$ equals $\square$ $\tan (\theta)$ equals $\square$ $\cot (\theta)$ equals $\square$

Solution

Solution Steps

Step 1: Identify the Quadrant

The angle $\theta$ lies in Quadrant III, based on its value.

Step 2: Calculate Trigonometric Values

Using the trigonometric identities, we find the values as follows:

$\sin(\theta) = -0.5$
$\cos(\theta) = -0.866$
$\tan(\theta) = 0.577$
$\cot(\theta) = 1.732$
$\sec(\theta) = -1.155$
$\csc(\theta) = -2$

Final Answer:

The trigonometric values for $\theta$ are $\sin(\theta) = -0.5$, $\cos(\theta) = -0.866$, $\tan(\theta) = 0.577$, $\cot(\theta) = 1.732$, $\sec(\theta) = -1.155$, and $\csc(\theta) = -2$.

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