High school trigonometry for physics

Navigation
Next:	Vectors
Previous:	Measurement
Up:	Topic: High School Physics

From Wikiversity

Jump to: navigation, search

[edit] Trigonometric Functions

A right-angled triangle where c₁ and c₂ are the catheti and h is the hypotenuse.

The following trigonometric functions are defined for all right triangles. A right triangle is a triangle in which one of the angles is right, in other words 90 degrees. The sum of the two other angles always adds up to 90 degrees. The longest side in the triangle is called the hypotenuse, and it is always opposite to the right angle. The two remaining sides are called cathetuses. A cathetus is either one of the two sides which are adjacent to the right angle.

To make use of the trigonometric functions listed below, one has to understand that each and every one of them is always performed on a desired angle. One can imagine "standing" in the desired angle. The adjacent cathetus is the side directly connected with the angle, and the opposite cathetus is the side furthest away (not connected to the specific angle in any way). The dilemma arises when one is standing in the right angle, since then both cathetuses are adjacent and neither is opposite. To understand, for instance, why cosinus for 90 degrees is defined, it is necessary to understand the basics of the unit circle. For a high-school physicist, however, it is often more important to get the raw data, in this case the length of a side or the size of a specific angle, than understanding the mathematics behind it.

$\sin \theta = { \mathrm{opposite} \over \mathrm{hypoteneuse} }$

$\cos \theta = { \mathrm{adjacent} \over \mathrm{hypoteneuse} }$

$\tan \theta = { \mathrm{opposite} \over \mathrm{adjacent} }$

$\cot \theta = \frac{1}{\tan\theta} = { \mathrm{adjacent} \over \mathrm{ opposite } }$

$\sec \theta = \frac{1}{\cos\theta}={ \mathrm{hypoteneuse} \over \mathrm{adjacent} }$

$\csc \theta = \frac{1}{\sin\theta} = { \mathrm{hypoteneuse} \over \mathrm{opposite} }$

[edit] Table of Common Angles

Degrees	Radians	Sine	Cosine	Tangent
$0 \,$	$0 \,$	${ 0 } \,$	${ 1 } \,$	$0 \,$
$30 \,$	${\pi \over 6}$	${ 1 \over 2 }$	${ \sqrt{3} \over 2 }$	${ 1 \over \sqrt{3} }$
$45 \,$	${\pi \over 4}$	${ \sqrt{2} \over 2 }$	${ \sqrt{2} \over 2 }$	$1 \,$
$60 \,$	${\pi \over 3}$	${ \sqrt{3} \over 2 }$	${ 1 \over 2 }$	${ \sqrt{3} }$
$90 \,$	${\pi \over 2}$	$1 \,$	$0 \,$	$undefined \,$