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

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 $\square$
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Solution

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Solution Steps

Step 1: Identify the Quadrant

The angle θ\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⁡(θ)=−0.5\sin(\theta) = -0.5
  • cos⁡(θ)=−0.866\cos(\theta) = -0.866
  • tan⁡(θ)=0.577\tan(\theta) = 0.577
  • cot⁡(θ)=1.732\cot(\theta) = 1.732
  • sec⁡(θ)=−1.155\sec(\theta) = -1.155
  • csc⁡(θ)=−2\csc(\theta) = -2

Final Answer:

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

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