trigonometry and its functions

1. Jul 31, 2019

3. Instant Trig
Trigonometry is math, so many people find it scary
It’s usually taught in a one-semester high-school
course
However, 95% of all the “trig” you’ll ever need to
know can be covered in 15 minutes
And that’s what we’re going to do now

4. Angles add to 180°
The angles of a triangle always add up to 180°
44°
68° 68°
20°
120°
30°
44°
68°
+ 68°
180°
20°
30°
180°
+ 130°

5. Right triangles
We only care about right triangles
A right triangle is one in which one of the angles is 90°
Here’s a right triangle:
We call the longest side the hypotenuse
We pick one of the other angles--not the right angle
We name the other two sides relative to that angle
Here’s the
right angle
hypotenuse
Here’s the angle
we are looking at
adjacent
opposite

6. The Pythagorean Theorem
If you square the length of
the two shorter sides and
add them, you get the square
of the length of the
hypotenuse
adj2
+ opp2
= hyp2
32
+ 42
= 52
, or 9 + 16 = 25
hyp = sqrt(adj2
+ opp2
)
5 = sqrt(9 + 16)

7. Ratios
Since a triangle has three
sides, there are six ways to
divide the lengths of the
sides
Each of these six ratios has a
name (and an abbreviation)
Three ratios are most used:
 sine = sin = opp / hyp
 cosine = cos = adj / hyp
 tangent = tan = opp / adj
The other three ratios are
redundant with these and
can be ignored
The ratios depend on the
shape of the triangle (the
angles) but not on the size
hypotenuse
adjacent
opposite hypotenuse
adjacent
opposite

8. Using the ratios
With these functions, if you know an angle (in addition to
the right angle) and the length of a side, you can compute all
other angles and lengths of sides
If you know the angle marked in red (call it A) and you
know the length of the adjacent side, then
tan A = opp / adj, so length of opposite side is given by
opp = adj * tan A
cos A = adj / hyp, so length of hypotenuse is given by
hyp = adj / cos A
hypotenuse
adjacent
opposite

9. The hard part
If you understood this lecture, you’re in great shape
for doing all kinds of things with basic graphics
Here’s the part I’ve always found the hardest:
Memorizing the names of the ratios
sin = opp / hyp
cos = adj / hyp
tan = opp / adj
hypotenuse
adjacent
opposite