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Complete the fundamental trigonometric
identities.
Show all work to verify the identity.
cot y(sec y  1)  1
2
2
Solve the oblique/scalene triangle by finding
all side lengths and angle measures.
Solve for all values of x.
2 cos x  1  0
Write the three Pythagorean fundamental
trigonometric identities.
Show all work to verify the identity.
sec   1
2

sin

2
sec 
2
Solve the oblique/scalene triangle by finding
all side lengths and angle measures.
Solve for all values of x.
3 cot x  1  0
2
Use fundamental trigonometric identities to
factor the expression.
csc   cot   3
2
Show all work to verify the identity.
1
1
2

 2 sec 
1  sin  1  sin 
Solve the oblique/scalene triangle by finding
all side lengths and angle measures.
Solve for all values of x.
tan 3x(tan x  1)  0
Complete the fundamental trigonometric
identities.
sin( u ) 
csc( u ) 
cos( u ) 
sec( u )
tan( u ) 
cot( u ) 
Show all work to verify the identity.
cos y
sec y  tan y 
1  sin y
Solve the oblique/scalene triangle by finding
all side lengths and angle measures.
Solve for all values of x.
2 sin x  2  cos x
2
Use fundamental trigonometric identities to
simplify the expression.
sin x cos x  sin x
2
Show all work to verify the identity.
tan x  tan x sec x  tan x
4
2
2
2
Solve the real world application problem.
The bearing from the Pine Knob fire tower to the Colt Station fire tower is
N65°E, and the two towers are 30 km apart. A fire spotted by rangers in each
tower has a bearing of N80°E from Pine Knob and S70°E from Colt Station.
Find the distance of the fire from each tower.
Solve for all values of x.
2 sin x  csc x  0
Complete the fundamental trigonometric
identities.


sin   u  
2



csc  u  
2



cos  u  
2



sec  u  
2



tan   u  
2



cot  u  
2

Show all work to verify the identity.
cot 
1  sin 

1  csc 
sin 
2
Solve the real world application problem.
The baseball player in center field is playing approximately 330 feet from the
television camera that is behind home plate. A batter hits a fly ball that goes to
the wall 420 feet from the camera. The camera turns 8° to follow the play.
Approximately how far does the center fielder have to run to make the catch?
Solve for all values of x.
cos x  sin x tan x  2
3
Given sec u   and
2
tan u  0 evaluate
the six trigonometric functions of u.
Show all work to verify the identity.
cos x  sin x tan x  sec x
Solve the real world application problem.
A bridge is to be built across a small lake from a gazebo to a dock. The bearing
from the gazebo to the dock is S41°W. From a tree 100 meters from the
gazebo, the bearings to the gazebo and the dock are S74°E and S28°E
respectively. Find the distance from the gazebo to the dock.
Solve for all values of x.
sec 4x  2
Manipulate fundamental trigonometric
identities to complete the expressions.
sin u 
2
sec u 
2
csc u 
2
Show all work to verify the identity.
csc( x)
  cot x
sec( x)
Solve the real world application problem.
A 100-foot vertical tower is erected on a hill that makes a 6° angle with the
horizontal. Find the length of each of the two guy wires that will be anchored 75
feet uphill and downhill from the base of the tower.