Transcript Trigonometry functions and Right Triangles

Trigonometry functions and
Right Triangles
First of all, think of a trigonometry function as
you would any general function. That is, a
value goes in and a value comes out.
f(x) = ?
• The names of the three primary
trigonometry functions are:
– Sine
– Cosine
– tangent
• These are abbreviated this way:
– sine.....sin
– cosine.....cos
– tangent.....tan
A value goes in and a value
comes out
• sin (Θ) = ?
• cos (Θ) = ?
• tan (Θ) = ?
• The input value is Θ. This input value
usually represents an angle.
Θ
• What does the output represent?
What do these have in common?
They have the same angle!!!
• The value for the sin(Θ) is defined as the value that
you get when you divide the opposite side by the
hypotenuse. This can be written:
– sin(Θ) = opposite / hypotenuse
– So the sin of the angle is simply the ratio between the opposite
side and the hypotenuse
– Since both triangles have the same angle the ratio between the
opposite side and the hypotenuse is the same!
• The three trig functions are simply the ratios
•
•
•
between the sides of a right triangle.
sin(Θ) = opposite / hypotenuse
cos(Θ) = adjacent / hypotenuse
tan(Θ) = opposite / adjacent
An easy was to remember which function goes
with each ratios is:
SOH CAH TOA
• A calculator looks up the ratio for the angle that
you enter.
example
• sin(Θ) = opp / hyp =
– 4.00 cm / 7.21 cm =
– 0.5548
• cos (Θ) = adj / hyp
• tan (Θ) = opp / adj
A= Θ = 33.7
Try typing sin(33.7) into
your calc.
It gives you the ratio.
Try one!
• Θ= 40o
hyp = 5.5cm
Θ
• Find the length of opposite side.
• sin(Θ) = opp / hyp
• Find the length of the adjacent side
• Multiple ways to do it.
What if you know two of the sides
but not the angle?
3cm
Θ
4cm
Θ=?