Right Triangles and Trig Ratios

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Transcript Right Triangles and Trig Ratios

Right Triangles and Trig Ratios
SOH-CAH-TOA
• SOH-CAH-TOA is an acronym used in Geometry and
Right Triangle Trig to remember what sides of a right
triangle go with which Trig Ratios
• Each angle value (radians and degrees) has a specific
ratio of sides that always holds true
Consider an angle whose terminal ray
passes through the point (4, 5)
• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q1)
Consider an angle whose terminal ray
passes through the point (-4, 5)
• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q2)
Consider an angle whose terminal ray
passes through the point (-4, -5)
• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q3)
Consider an angle whose terminal ray
passes through the point (4, -5)
• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q4)
Trig Definitions/Ratios
• Since the opposite always refers to the vertical
distance and the adjacent always refers to the
horizontal distance, we can say that…
y
sin  
r
x
cos  
r
y
tan  
x
Sign Analysis Chart
Examples
• Tell whether each of the following is positive
or negative:
sin 240 
Examples
• Tell whether each of the following is positive
or negative:
sin 240 
cos 300

Examples
• Tell whether each of the following is positive
or negative:
sin 240 
3
tan
4
cos 300

Examples
• Tell whether each of the following is positive
or negative:
sin 240 
cos 300
3
tan
4
 4 
sin  

 3 

Finding Exact Values
• If  is a
quadrant angle
find sin  and cos
4th
5
and tan   
12
,
Finding Exact Values
• An angle has a terminal ray that passes through the
point (-4, 7). Find the exact value of the three trig
ratios in simplest form.
The Unit Circle
(Quadrantal Angles)
• Consider a circle with radius = ____
– What is the sin 90?
– Does the size of the circle matter when evaluating the trig
ratios?
The Unit Circle
(Quadrantal Angles)
Examples
• Find the exact value for each of the following:
sin 270 
Examples
• Find the exact value for each of the following:
sin 270

tan 90

Examples
• Find the exact value for each of the following:
sin 270

cos  
tan 90

Examples
• Find the exact value for each of the following:
sin 270 
tan 90 
cos  
 5 
sin  
 2 
Homework
• Pg. 272 (1 – 27odd)