Question 35485
ANGLE =15*PI/4=16*PI/4-PI/4=-PI/4....THAT IS WE TAKE TRIANGLE WITH ANGLE PI/4 AND APPLY THE RULE OF SIGNS..."ALL SILVER TEA CUPS"...THAT IS IT IS AN ISOCELLES RIGHT ANGLED TRIANGLE.HENCE LET BOTH  SIDES BE 1 EACH. THEN HYPOTENUSE =SQRT(1^2+1^2)=SQRT(2)
SO 
SIN (PI/4)=1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
COSEC(PI/4)=SQRT(2)=1.4142
COS(PI/4)= 1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
SEC(PI/4)=SQRT(2)=1.4142
TAN(PI/4)=1/1=1
COT(PI/4)=1/1=1

HENCE 

SIN (-PI/4)=-1/SQRT(2)=-SQRT(2)/2=-1.4142/2=-0.7071
COSEC(-PI/4)=-SQRT(2)=-1.4142
COS(-PI/4)= 1/SQRT(2)=SQRT(2)/2=1.4142/2=0.7071
SEC(-PI/4)=SQRT(2)=1.4142
TAN(-PI/4)=-1/1=-1
COT(-PI/4)=-1/1=-1