Finding arccos(-√3/2)

Trigonometry · Axiom Academy

Understanding the range of inverse cosine and using it to identify the correct quadrant Excellent work! You've successfully found arccos(-√3/2) = 5π/6. Here's what we learned: Range Restriction: The arccos function always returns values in [0, π]. This means Quadrants I and II only. Sign Analysis: Since cosine is negative and we're restricted to [0, π], the answer must be in Quadrant II (where π/2 < θ < π). Reference Angle Method: Find the positive reference angle first (where cos = √3/2 gives π/6), then use π - π/6 to get the Quadrant II angle. Always Verify: Check that your answer is in the correct range and produces the original value when you apply cosine to it. This range-based approach is essential for all inverse trig functions. Remember: arcsin uses [-π/2, π/2], arccos uses [0, π], and arctan uses (-π/2, π/2). Understanding these ranges helps you determine the correct quadrant every time!

This is the written version of the interactive lesson above. See the full Trigonometry course.