Embed Size (px)
Citation preview
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.
– Use equal cofunctions of complements
– Use right triangle trig. to solve applied problems
3,4,6
These relationships holds true for ALL right triangles
sin
cos
sintan
cos
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
csc
sec
coscot
sin
hypotenuse
opposite
hypotenuse
adjacent
adjacent
opposite
1. Given this right triangle
Find the value of all six trig. functions of Θ. Make sure each value is in simplified form.
C
B
A
b
a = 1
c = 5
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:
1
radius
2
2
2
2
45o
45o
90o
1
radius
90o
3
2
1
2
30o
60o
3
6
4
4
Special Triangles
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
8. csc
3
6
Cofunction Identities, radians Cofunction Identities, degrees
sin (90° – x) = cos x
cos (90° – x) = sin x
tan (90° – x) =
cot xcot (90° – x) = tan x
sec (90° – x) = csc x
csc (90° – x) = sec x
Cofunction IdentitiesTrig 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.
Find a cofunction with the same value as the given expression.
9. sin 46o 10. cot 12
OR
C
B
A = 24o
b = 750 yd
a
c
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?
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
