Download Fundamental Trigonometry Concepts needed for Calculus

Fundamental Trigonometry Concepts Needed for Calculus
sin A =
a y opp
 
c r hyp
cos A =
b x adj
 
c r hyp
tan A =
a y opp
 
b x adj
cot A =
b x adj
 
a y opp
1. Reciprocal Functions: csc A =
1
;
sin A
sec A =
cot A =
c r hyp
 
b x adj
1
;
tan A
csc A =
sec A =
c r hyp
 
a y opp
1
cos A
2. Cofuntions: sin & cos, tan & cot, sec & csc. Any function of an angle less than 90 is equal to the
cofunction of its complement (i.e. 90 - A).
3. Signs on the trig functions I the four quadrants are:
All trig functions are positive in Q I.
cos and sec are negative in Q II and Q III
sin & csc are negative in Q III & Q IV
tan and cot are negative in Q II and Q IV
4. To take the function of an angle A greater than 90 and reduce it to the same function of an angle less
than 90 first determine the sign on that function in that particular quadrant and then:
i) if A is in Q II, use 180 - A;
ii) if A is in Q III, use A - 180;
iii) if A is in Q IV use 360 - A.
5. FUNDAMENTAL RELATIONSHIPS:
sin (-) = - sin ; cos (-) = cos ;
sin2 + cos2 = 1 for all .
cos(   )  cos  cos   sin  sin 
sin(    )  sin  cos   cos  sin 
tan2 + 1 = sec2 & 1 + cot2 = csc2
1  cos 2
1  cos 2
cos 2  
sin 2  
cos 2 = cos2 - sin2;
sin 2 = 2 sin  cos ;
;
2
2
R
D

7.Relationship between degrees and radians (a pure number, no units):
; R-radians; D-degrees
 180 o
8. Basic trig values:
or
6. Other relationships that follow from (5) above are:
sin 0 =
0 /2 = 0.000 = cos 90
sin /6 = 1 /2 = 0.500 = cos 60
sin
0  0
0
30  /6
1/2
cos
1
45  /4
2 /2
2 /2
1
60  /3
3 /2
1/2
3 /3
2
23 /3
sin /4 =
2 /2 = 0.707 = cos 45
tan
0
sin /3 =
3 /2
3 /3
3 /2 = 0.866 = cos 30
cot
--
3
1
sin /2 =
4 /2 = 1.000 = cos 0
sec
1
2
csc
--
2 3 /3
2
2
3
90  /2
1
0
-0
-1