12 grade maths others
Find the principal value of: cos⁻¹(−1/(√2))
Find the principal value of: cos⁻¹(−1/(√2))
1 Answer
Askiitians Tutor Team
Approved Tutor Answer9 Months agoThe principal value of the inverse cosine function, cos⁻¹(x), is the angle whose cosine is x, typically within the range of 0 to π (0 to 180 degrees).
Finding the Value
To find the principal value of cos⁻¹(−1/(√2)), we need to determine the angle where the cosine equals −1/(√2).
Identifying the Angle
- The cosine of 135 degrees (or 3π/4 radians) is −1/(√2).
- This angle lies within the specified range for the principal value.
Final Result
Thus, the principal value of cos⁻¹(−1/(√2)) is 3π/4 radians or 135 degrees.
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