Download 4.3 Right Triangle Trigonometry - abu-saba

4.3
Right Triangle Trigonometry
Pg. 484 # 6-16 (even), 22-34 (even), 54-60 (even)
– Use right triangles to evaluate trigonometric functions
– Find function values for 30 degrees, 45 degrees & 60 degrees. Otherwise
known as,      in radians.
,
,


6 4 3
– Use equal cofunctions of complements
– Use right triangle trig. to solve applied problems
These relationships holds true for ALL right triangles
opposite
sin  
hypotenuse
adjacent
cos  
hypotenuse
sin  opposite
tan  

cos  adjacent
hypotenuse
csc  
opposite
sec  
hypotenuse
adjacent
cot  
cos  adjacent

sin  opposite
1.
Given this right triangle
c= 5
A
B
a=1

b
C
Find the value of all six trig. functions of Θ.
Make sure each value is in simplified form.
Special Triangles
All 45o - 45o - 90o triangles on a unit
All 30o - 60o - 90o triangles on a unit
circle have these side lengths:
circle have these side lengths:

6

4
45
o
2
2
radius
radius
30o
1
90o
45o
2
2
1
3
2

4
90o
60 o
1
2

3
Using the figures only, find the following values:
2. tan 30o
3. cos 60o
4. sin 45o
5. sec 60o
6. cot 45o
7. sin 
3
8. csc 
6
Cofunction Identities
Trig identities showing the relationship between sine and cosine, tangent and
cotangent, and secant and cosecant. The value of a trig function of an angle
equals the value of the cofunction of the complement of the angle.
Cofunction Identities, radians
Cofunction Identities,
degrees
OR
sin (90° – x) =
cos x
cos (90° – x) =
sin x
tan (90° – x) =
cot x
cot (90° – x) =
tan x
sec (90° – x) = csc (90° – x) =
csc x
sec x
Find a cofunction with the same value as the given expression.
9. sin 46o
10. cot

12
11. The distance across a lake (a) is unknown. To find the distance, a surveyor
took the measurements shown in the figure. What is the distance across the lake?
c
 = 24o
A
b = 750 yd
B
a
C
12. A flagpole that is 14 meters tall casts a shadow 10 meters long. Find the
angle of elevation of the sun to the nearest degree.
Angles of Elevation:
Angles of Depression:
Rotate from a horizontal UP
Rotate from a horizontal DOWN