Download Trigonometric Ratios in Right Triangles

1.3 Right Triangle
Trigonometry
Part 2
Another way to look at
trig functions is from a
right triangle perspective!
Using the lengths of the sides, you can define
the 6 trigonometric functions of the acute angle θ
0 < θ < 90°
q
For such angles the value of each trig function is
positive!!!!!
The SOH-CAH-TOA model
q
Opposite
sin θ 
Hypotenuse
Adjacent
cosθ 
Hypotenuse
Opposite
tanθ 
Adjacent
The Six Trigonometric Ratios
Opposite
Hypotenuse
Adjacent
cosθ 
Hypotenuse
Opposite
tanθ 
Adjacent
sin θ 
q
Hypotenuse
Opposite
Hypotenuse
secθ 
Adjacent
Adjacent
cotθ 
Opposite
cscθ 
The Cosecant, Secant, and Cotangent of q
are the reciprocals of
the Sine, Cosine and Tangent of q.
Example: Evaluating
Trigonometric Functions
 Find the values of
the 6 trig functions.
hypotenuse
θ
3
 First of all, we need to find
the value of the
hypotenuse.
 Use the Pythagorean
4
theorem.
 c2 = a2 + b2
 c2 = 42 + 32
 c2 = 16 + 9 = 25
 c = 25 = 5 = hypotenuse
Example: Evaluating
Trigonometric Functions
 Find the values of
the 6 trig functions:
5
4
θ
3
opp 4
sin q 

hyp 5
hyp 5
csc q 

opp 4
adj 3
cos q 

hyp 5
hyp 5
sec q 

adj 3
opp 4
tan q 

adj 3
adj 3
cot q 

opp 4
Explorations w/ the 6 Basic Trig Ratios
sin q
?
 Which trig function is
tan θ
cos q
 Which trig function is csc q ?
sec θ
cot q
 What is the product of all 6 multiplied together?
 Which two trig ratios must be less than 1 for any
acute angle and why?
 Hint: what is always the longest side of the right
triangle?
sin θ and cos θ
1
Classwork/Homework
 Finish up Pythagorean Theorem Proofs
 Worksheet – Right Triangle Trig: Evaluating
Trig Ratios