Why are my trigonometry answers wrong?

Nearly always the angle mode. Check by computing sin(30): it should be exactly 0.5 in degrees. Anything else means you are in radians or gradians.

What is the difference between log and ln?

Here log is base 10 and ln is base e, about 2.718. ln(100) is 4.605 and log(100) is 2. Be careful moving between calculators and code, where log() usually means the natural log.

How do I enter scientific notation?

Use the EE or EXP key, which already supplies the '× 10 to the'. For 6.02 × 10²³, press 6.02, then EE, then 23.

The angle subtended by an arc equal to the radius. A full circle is 2π radians, so 180 degrees is π. Calculus and most programming languages use radians throughout.

How do I find an inverse trig function?

Use the shift or 2nd key before sin, cos or tan to get arcsin, arccos or arctan. They convert a ratio back into an angle.

How many digits should I keep?

Round to the significant figures your inputs justify. A measurement to three significant figures cannot produce an answer good to ten, whatever the display shows.

What does the M+ key do on a scientific calculator?

Adds the displayed value to memory, the same as on a basic model. On scientific calculators there are often several memory registers, addressed by letter.

Why does my calculator show an error for tan(90)?

Because tangent is undefined there — it requires dividing by zero. The function grows without limit as the angle approaches 90 degrees.

Scientific Calculator

Evaluate expressions with powers, roots, logs, and trig.

About the Scientific Calculator

Trigonometry, logarithms, powers and roots in one expression, for when a basic calculator runs out of buttons.

How to use it

Type the expression using sin, cos, tan, log, sqrt.
Use ** for powers, as in 2**10.
Parentheses group operations.

The formula

A scientific calculator adds three things a basic one lacks: functions, exponent notation, and an angle mode that silently changes every trigonometric answer.

log = base 10 · ln = base e (2.71828…)
EE / EXP enters × 10ⁿ · 6.02 EE 23 = 6.02 × 10²³

The log distinction catches people constantly. In most calculators and spreadsheets log means base 10 while ln means natural log — but in nearly every programming language, log() is the natural logarithm. Getting them confused changes an answer by a factor of 2.303.

The angle mode is the other silent hazard. DEG, RAD and GRAD are three different units, and nothing on screen shouts about which is active. sin(30) is 0.5 in degrees and −0.988 in radians, and both look like plausible calculator output.

Worked examples

Entry	In DEG mode	In RAD mode	Note
sin(30)	0.5	−0.988	the classic mode error
cos(0)	1	1	agrees — no help in spotting the mode
log(100)	2	2	base 10, unaffected by angle mode
ln(100)	4.605	4.605	base e — 2.303 times larger

The second row is the dangerous one. cos(0) returns 1 in every angle mode, so the check most people reach for proves nothing at all. Use sin(30) instead: if it returns 0.5 you are in degrees, and if it returns anything else you are not. It takes two seconds and it catches the error that ruins whole worksheets.

Common mistakes

Leaving the calculator in the wrong angle mode. The most common scientific calculator error by a wide margin. Test with sin(30) before starting any trigonometry — it should be exactly 0.5.
Confusing log with ln. Here, log is base 10 and ln is base e. In most programming languages log() means the natural log, which is a factor of 2.303 different.
Misusing the EE key. EE already means '× 10 to the'. Entering 6.02 × 10 EE 23 gives 6.02 × 10²⁴, an answer ten times too large.
Trusting every digit on the display. A ten-digit readout does not mean ten significant figures of accuracy. Your answer can be no more precise than the least precise measurement that went into it.

Terms explained

DEG / RAD / GRAD: The three angle modes. A full circle is 360 degrees, 2π radians or 400 gradians.
Natural logarithm: Logarithm to base e, written ln. Appears throughout growth, decay and compound interest.
Scientific notation: Writing numbers as a coefficient times a power of ten. Entered with the EE or EXP key.
Significant figures: The digits carrying real information. Results should be rounded to match the least precise input.
Inverse function: Reached with the shift or 2nd key: arcsin, arccos, arctan, and the exponential functions that undo the logs.
Mantissa: The coefficient part of a number in scientific notation — the 6.02 in 6.02 × 10²³.

Common questions

Why are my trigonometry answers wrong?: Nearly always the angle mode. Check by computing sin(30): it should be exactly 0.5 in degrees. Anything else means you are in radians or gradians.
What is the difference between log and ln?: Here log is base 10 and ln is base e, about 2.718. ln(100) is 4.605 and log(100) is 2. Be careful moving between calculators and code, where log() usually means the natural log.
How do I enter scientific notation?: Use the EE or EXP key, which already supplies the '× 10 to the'. For 6.02 × 10²³, press 6.02, then EE, then 23.
What is a radian?: The angle subtended by an arc equal to the radius. A full circle is 2π radians, so 180 degrees is π. Calculus and most programming languages use radians throughout.
How do I find an inverse trig function?: Use the shift or 2nd key before sin, cos or tan to get arcsin, arccos or arctan. They convert a ratio back into an angle.
How many digits should I keep?: Round to the significant figures your inputs justify. A measurement to three significant figures cannot produce an answer good to ten, whatever the display shows.
What does the M+ key do on a scientific calculator?: Adds the displayed value to memory, the same as on a basic model. On scientific calculators there are often several memory registers, addressed by letter.
Why does my calculator show an error for tan(90)?: Because tangent is undefined there — it requires dividing by zero. The function grows without limit as the angle approaches 90 degrees.

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