Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Find the value of cos⁻¹ (cos7π/6).

Sagot :

Answer:

5π/6

Step-by-step explanation:

Given :

  • cos⁻¹ (cos7π/6)

Solving :

  • We know that : cos⁻¹ cosθ = θ
  • But we can't just do that in this case
  • Because the range of cos values is [0, π]
  • Clearly, our value does not lie in this range
  • We have to take a different Quadrant other than the 3rd Quadrant which gives cos a negative value
  • The 2nd Quadrant also has cos values negative
  • Therefore,
  • cos⁻¹ cos (π - π/6)
  • cos⁻¹ cos (5π/6)
  • ⇒ 5π/6 ∈ [0, π] ⇒ It lies in the range!
blommock

Answer:

5π Over 6

Step-by-step explanation:

You can write  7π6 as (π+π6)Thus we can clearly see the angle falls in the third quadrant. And the cosine value in third quadrant is always negative. Hence, cos(π+π6)=−cos(π6)coming back to the question cos−1[cos(7π6)]=cos−1[−cos(π6)]=π−cos−1[cos(π6)]=π−π6=5π6

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.