Trigonometry depends heavily on calculator mode. The most common problem is not the sine or cosine key; it is using Degree mode when the assignment expects radians, or Radian mode when it expects degrees.
Check angle mode first
Before using sine, cosine or tangent, open MODE and check Degree or Radian. Geometry classes often use degrees. Precalculus and calculus often use radians.
If sin(30) does not look like 0.5, you are probably in Radian mode.
Basic trig functions
Use sin, cos and tan for the main trigonometric ratios.
Close parentheses when entering more complex expressions, especially when trig functions are part of fractions or equations.
Inverse trig functions
Inverse sine, cosine and tangent are usually accessed with 2nd plus the trig key. These functions return angles.
The returned angle follows the current Degree/Radian setting. Check the mode before interpreting the answer.
Graphing trig functions
Use Y= to graph functions such as sin(X) or cos(X). Window settings are especially important for trig graphs because periods and amplitudes matter.
In radian mode, a useful x-window might involve multiples of π. In degree mode, use windows such as 0 to 360 for one full cycle.
Common trig mistakes
Using the wrong angle mode, forgetting parentheses, entering inverse trig incorrectly and mixing degrees with radians are the most common errors.
Write down the expected unit before calculating: degrees, radians or unitless ratio.
Quick reference table
| Task | Check |
|---|---|
| sin, cos, tan | Degree/Radian mode |
| inverse trig | Returned unit follows mode |
| graph trig | Window should match period |
| radian problems | Use π-based values when possible |
| degree problems | Use degree mode and degree windows |