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Section 5.4: Right Triangle Trigonometry Right triangle: 0 90 Acute angle: Ex: Given Find the exact values of all Trig. Functions. 2 4 Complementary Angles: ( Cofunctions ) Two acute angles are called complementary if their sum is a right angle. sin cos c b a Ex: sin(90 ) 2) cos(90 ) 3) tan(90 ) 4) csc(90 ) 1) Ex: 1) sin 65 2) tan 12 Reference Angle: Is the acute angle terminal side and the x axis R (always taken positive) between the Ex: Find the reference angles for the following angles. 1) 135 , 2) 7 11 13 , 3) 310 , 4) , 5) 6 9 8 ___________________________________________________________________ Ex: Find the exact values of 2 11 ) , 4) tan( ) 3 6 2 2 , 6) 1 tan 5 csc 85 5) tan12 cot 78 7) cos35 sin 55 sin 35 cos55 tan 2 40 1 tan 2 20 sin 70 8) , 9) 2 2 cot 50 cos 50 sec 20 1) cos 210 , 2) csc 300 , 3) sin( ___________________________________________________________________ Ex: If 1) cot 2 , find the exact values of tan , 2) csc 2 , 3) tan( ) , 4) sec 2 2 Ex: Answer True or False 13 cos( ) cos( ) , 7 7 4 11 7 ) tan( ) , 4) sec( ) sec( ) 3) tan( 5 5 18 18 1) sin( 7 ) sin( ) , 8 8 2) ___________________________________________________________________ _ Ex: Evaluate the followings 15 3 7 tan 2 ( ) csc 2 ( ) sin 2 ( ) 8 8 6 4 11 2 ) cos 2 ( ) cos 2 ( ) 2) cot ( 3 9 18 1)