Other Trigonometric Functions

Sin q = y/r   (sine)                                      Csc q = r/y (cosecant),  y ¹ 0

Cos q = x/r  (cosine)                                   Sec q = r/x  (secant) ,  x ¹ 0

Tan q = y/x (tangent) , x ¹ 0                       Cot q = x/y  (cotangent), y ¹ 0

Quotient Identities

tan q = sin 0                 cot q = cos q
            cos 0                              sin q

Reciprocal Identities

tan q =     1               cot q =    1
             cot q                        tan q

sin q =    1                csc q =    1
            csc q                         sin q

cos q =    1               sec q =    1
            sec q                         cos q

Signs of Trigonometric Functions

ALL STUDENTS TAKE CALCULUS -- the trigonometric functions named in each quadrant are positive in those quadrants
 
II   S

Sin

Csc

 I       A

All

Functions
III      T

Tan

Cot

 IV    C

Cos

Sec

Graphs

y = tan x   for    -p/2 < x < p/2
Domain:   x is all real numbers except p/2 + np  (asymptotes occur at these values)
Range:  all real numbers
Period:  p
 

y=cot x  for   0 < x < p
Domain:  all real numbers except np  (asymptotes occur here)
Range:  all real numbers
Period:  p

y = sec x   for    0 < x < 2p
Domain:   x is all real numbers except p/2 + np  (asymptotes occur at these values)
Range:  all real numbers
Period:  2p

y = csc x    for    0 < x < 2p
Domain:  all real numbers except np  (asymptotes occur here)
Range:  all real numbers
Period:  2p


Problems

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