Wrong mode turns a correct ratio into a nonsense angle. Check DEG before sin⁻¹.
Key formulas
Symptom
You expect about 30° and the screen shows 0.52 — that is radians. Switch mode and recompute.
Inverse trig range
sin⁻¹ returns between −90° and 90°. For an obtuse angle in a triangle, use the sine rule carefully or work from 180°−α.
Habit
Glance at the DEG/RAD indicator every time you open a trigonometry question.
Worked example
Worked example
Problem. You compute tan⁻¹(1) and see 0.785398. What is wrong, and what is the correct angle in degrees?
Solution. The calculator is in radian mode. Switch to DEG. tan⁻¹(1) = 45°.
Quick test
tan⁻¹(1) should be 45 in degree mode.
Review quiz
Before pressing sin⁻¹ in a geometry paper you should check:
Practice questions
- What does tan⁻¹(1) return in radian mode approximately?
- Describe how to get an obtuse angle from an acute inverse-sine result.
Study notes
Does π in a formula mean radians?
π as a number in an expression is fine; trig function arguments still follow the mode.