Transcript Right Triangles and the Trigonometric Functions

Right Triangles
Right triangles are the basis of the
trigonometric functions which we are
going to study.
There are six trigonometric functions for
which we need to know the definitions.
We will start with two of them.
Don’t forget the Pythagorean theorem! 
Sine and Cosine
Sine and cosine are two of the
trigonometric functions.
Their argument is an angle (i.e., θ) and
their output is a value.
This value is a ratio of two sides of a right
triangle.
Labeling Sides
Labeling Sides
Labeling sides is important because we
need to know which sides we are referring
to in relation to which angle.
If θ was the other angle in the triangle
shown in the previous slide, the adjacent
and opposite sides would be switched.
This is important for the definitions of the
sine and cosine.
Sine and Cosine
opp
sin  
hyp
adj
cos  
hyp
Sine and Cosine
4
sin  
5
3
cos  
5
Sine and Cosine
17
sin   cos  
17
4 17
cos   sin  
17
The Six Trigonometric Functions
Sine
Cosecant
opp
sin  
hyp
1
hyp
csc  

sin  opp
Cosine
Secant
adj
cos  
hyp
1
hyp
sec  

cos  adj
Tangent
Cotangent
sin  opp
tan  

cos  adj
1
cos  adj
cot  


tan  sin  opp
Example
Example Solutions
5 29
sin  
29
2 29
cos  
29
5
tan  
2
29
csc  
5
29
sec  
2
2
cot  
5