Trigonometry. 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. 20°. 44°. 30°. 120°. 68°.
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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 angle
we are looking atRight triangles
adj2 + opp2 = hyp2
32 + 42 = 52, or 9 + 16 = 25
hyp = sqrt(adj2 + opp2)
5 = sqrt(9 + 16)The Pythagorean Theorem
3-4-5 and itsmultiples (6-8-10, etc.)are the best known
5-12-13 and its multiples form another set
25 + 144 = 169
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
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 byopp = adj * tan A
cos A = adj / hyp, so length of hypotenuse is given byhyp = adj / cos A
adjacentUsing the ratios
adjDrawing a “Turtle”
You want to move h units in theangle direction, to (x1, y1):
You are at: (x, y)
So you make a right triangle...
And you label it...
And you compute: x1 = x + adj = x + hyp * (adj/hyp) = x + hyp * cos
y1 = y - opp = y - hyp * (opp/hyp) = y - hyp * sin
This is the first point in your “Turtle” triangle
Find the other points similarly...