Question

Find the value of cos⁻¹ (cos7π/6).

Answer 1

5π Over 6

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

Answer 2

5π/6

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!