TAN: Your Angle's Best Friend (and a Bit of a Daredevil)
Need to find the tangent of an angle? Look no further than the TAN
command, your angle's best friend (but with a bit of a daredevil streak)! This trigonometric function takes an angle (in radians) and returns its tangent value, a key ingredient in understanding the relationships between angles and sides in right triangles, as well as in modeling slopes and rates of change. Just be careful, because TAN
can sometimes get a bit wild with certain angles!
Syntax
TAN(<angle>)
Where:
- <angle>
: The angle (in radians) for which you want to find the tangent.
Applications
The TAN
command is your go-to tool when:
- Working with right triangles: Find the ratio of the opposite side to the adjacent side, given an angle.
- Calculating slopes and gradients: Tangents represent the steepness of a line or surface.
- Modeling rates of change: The tangent function is related to derivatives in calculus, used to describe how quantities change over time.
- Creating games and simulations: Calculate trajectories, angles of reflection, and other movements based on angles.
Code Examples
1. Simple Tangent Calculation:
10 PI=3.141592653
20 R = PI/4 :rem Angle of 45 degrees in radians
30 T = TAN(R) :rem T stores the tangent of the angle
40 PRINT T :rem Output: 1
This example demonstrates how to find the tangent of 45 degrees (which is 1).
2. Finding Slope:
10 PI=3.141592653
20 INPUT "Enter rise: "; Y
30 INPUT "Enter run: "; X
40 IF X=0 THEN PRINT "Undefined slope!": END :rem Avoid division by zero
50 M=Y/X :rem Slope is rise over run
60 A=ATN(M)*180/PI :rem Calculate the angle in degrees using ATN
70 PRINT "Angle of slope: "; A; " degrees"
This code calculates the angle of a slope based on the rise and run.
TAN in the Wild: The Rollercoaster Engineer
Imagine you're designing a thrilling rollercoaster. The TAN
command can help you calculate the steepness of the drops and curves, ensuring a safe yet exhilarating ride for your passengers!
Don't be afraid to embrace the thrill of trigonometry! With TAN
by your side, you can conquer angles and ratios, opening up a world of possibilities in mathematics, physics, and beyond. Just remember, TAN
can be a bit unpredictable when dealing with certain angles (like 90 degrees), so be sure to handle those special cases with care. Let TAN
be your guide to a world of exciting calculations and thrilling applications!
Key Points to Remember:
- In Commodore 64 BASIC, angles are measured in radians, not degrees. To convert degrees to radians, multiply by
PI/180
. - The
TAN
function can return very large or small values, even infinity for certain angles. - Use
TAN
responsibly and be prepared for potential?DIVISION BY ZERO ERROR
if you try to calculate the tangent of angles like 90 or 270 degrees.