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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

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