Download Notes 6.2 – Right Triangle Trig. Date: ______ Algebra III Honors

Notes 6.2 – Right Triangle Trig.
Algebra III Honors
Date: _________
Goal:
Trigonometric functions can be thought of as another way to measure angles. The functions
are the ratio of the sides formed by a given angle. So, if the angle is set, then the sides will
always form certain ratios.
sin  
csc  
cos  
sec  
tan  
cot  
Example 1: Find all six trigonometric function values for a 45 angle.
Example 2: Find all the trigonometric functions values for a 30 and 60 angle.
Example 3: Use a calculator to evaluate the following trig function values:
a) sin 76.4
b) sec 32.7
c) tan 145
d) cot 398
e) cos 3.5
f) csc 0.5
g) sin 2.1
h) cot 2π
Reciprocal Identities
1
1
tan x 
, cot x 
,
cot x
tan x
sin x 
1
,
csc x
csc x 
1
,
sin x
cos x 
1
,
sec x
sec x 
1
cos x
Pythagorean Identities
sin 2   cos 2   1
1  tan 2   sec 2 
1  cot 2   csc 2 
Quotient Identities
sin 
 tan 
cos 
cos 
 cot 
sin 
Example 4: Let θ be an acute angle such that sin θ = 0.6; find the values of a) cos θ and b) tan θ.
Example 5: Let θ be an acute angle such that tan θ = 1/3 find the values of a) cot θ, and b) sec θ.
Example 6: Use the trigonometric identities to transform the left side of the equation in to the
right side of the equation.
a) sin θcsc θ = 1
b) (csc θ + cot θ)(csc θ – cot θ) = 1
Applications
Example 7: A surveyor is standing 115 feet from the base of the Washington Monument. The
surveyor measures the angle of elevation to the top of the monument as 78.3 . How tall is the
Washington Monument?
Example 8: A historic lighthouse is 200 yards from a bike path along the edge of a lake. A
walkway to the lighthouse is 400 yards long. Find the acute angle θ between the bike path and
the walkway.
Homework: p. 443 – 445 # 4 – 64 M4 # 67, 70
Notes 6.2 – Right Triangle Trig.
Algebra III Honors
Name: __________
Date: _________
Skills Check. All problems are no calculator unless otherwise specified.
Find the exact value for the following trig functions.
1) sec 45
2) sin 30
3) cos 60
Find the approximate values for the following: (Calculator)
4) cos 24.5
5)
csc 125.7
6) cot 2.3
7) Let θ be an acute angle such that cos θ = 0.25, find the values of a) sin θ and b) tan θ.
8) Use trig identities to transform the left side into the right side of the equation:
tan θ csc θ = sec θ
9) You are standing 45 meters from the base of the Empire State building. You estimate that the
angle of elevation to the top of the 86th floor (the observatory) is 82 . The total height of the
building is another 123 meters above the 86th floor. What is the approximate height of the
building? (Calculator)