WELCOME TO A LESSON ON GRAPHING
THE SINE, COSINE AND TANGENT FUNCTIONS
ON THE TI84 GRAPHING CALCULATOR.
SO THE GOAL -- TODAY WAS TO BE ABLE TO GRAPH Y = COSINE X
ON THE GRAPHING CALCULATOR AS WE SEE HERE BELOW,
AS WELL AS GENERATE THE TABLE AS WE SEE HERE IN DEGREE
AND RADIAN MODE.
AND WE WANT TO BE ABLE TO DO THE SAME FOR Y - SINE X
AND Y = TANGENT X.
SO LET'S GO AHEAD AND GET OUR GRAPHING CALCULATOR OUT.
LET'S FIRST GRAPH THESE IN DEGREE MODE.
SO LET'S PRESS THE MODE KEY.
WE'LL GO DOWN TO ROW 3 AND HIGHLIGHT DEGREE
AND THEN PRESS ENTER.
SO IF WE'RE GOING TO GRAPH THEM IN DEGREE MODE,
WE FIRST HAVE TO SET UP THE WINDOW
AS WELL AS THE TABLE SET.
LET'S PRESS THE WINDOW KEY.
BECAUSE THE PERIOD OF COSINE AND SINE IS 36Y0 DEGREES,
LET'S SET OUR X MIN AND X MAX TO -360 TO +360.
THEN WE'RE GOING TO SCALE IT BY INCREMENTS OF 15 DEGREES.
AND THEN THE MINIMUM AND MAXIMUM VALUES
FOR COSINE AND SINE ARE -1 AND +1,
SO GO AHEAD AND LEAVE THE Y MIN AT -2 AND THE Y MAX AT +2.
NEXT LET'S GO AHEAD AND SET UP OUR TABLE OF VALUES.
SO WE'RE GOING TO PRESS SECOND WINDOW.
WE'LL HAVE THE TABLE START AT 0 DEGREES
AND AGAIN LET'S HAVE IT CHANGE BY INCREMENTS OF 15 DEGREES.
AND NOW WE'RE PRETTY MUCH SET TO GO.
LET'S GO AHEAD AND PRESS Y = AND ENTER IN OUR FUNCTIONS.
SO Y1 IS GOING TO BE COSINE X,
AND LET'S GO AHEAD AND PRESS GRAPH.
AND HERE'S A NICE GRAPH OF Y = COSINE X
SHOWING TWO PERIODS OF THE FUNCTION
AND IF WE PRESS SECOND GRAPH,
THE X COLUMN REPRESENTS THE ANGLE AND DEGREES
AND Y1 WOULD BE THE COSINE FUNCTION VALUE.
NOW NOTICE THE CALCULATOR ONLY GIVES US
THE DECIMAL APPROXIMATIONS FOR THE IRRATIONAL VALUES
OF ANY OF THE TRIG FUNCTIONS.
LET'S GO AHEAD AND GRAPH Y = SINE X,
WHAT WE'RE GOING TO DO IS ACTUALLY JUST TURN THIS OFF
BY GOING OVER TO THE EQUAL SINE AND THEN PRESS ENTER.
AND NOW IT'S NO LONGER HIGHLIGHTED.
LET'S PRESS THE DOWN ARROW AND THEN Y = SINE X AND Y2.
NOW IF WE PRESS GRAPH BECAUSE ONLY SINE X IS HIGHLIGHTED,
IT'S ONLY GOING TO GRAPH THE SINE FUNCTION
AND AGAIN IT'S GRAPHING THE FUNCTION
AND SHOWING TWO PERIODS.
NOW IF WE PRESS SECOND GRAPH,
AGAIN X REPRESENTS THE ANGLE AND DEGREES
AND NOW Y2 WOULD BE THE SINE FUNCTION VALUE.
LET'S GO BACK TO Y = JUST FOR A MOMENT.
IF WE TURN THEM BOTH ON AT THE SAME TIME
BY PRESSING ENTER HERE,
AGAIN NOTICE BOTH EQUAL SIGNS ARE DARKENED.
IF WE GO BACK TO THE TABLE NOW BY PRESSING SECOND GRAPH,
Y1 IS THE COSINE FUNCTION VALUES,
Y2 ARE THE SINE FUNCTION VALUES.
SO THESE ACTUALLY REPRESENT THE COORDINATES OF POINTS
ON THE UNIT CIRCLE.
THIS COLUMN WOULD BE THE X COORDINATES
AND THIS COLUMN WOULD BE THE Y COORDINATE
BECAUSE THESE ARE THE COSINE FUNCTION VALUES
WHICH EQUAL TO X ON THE UNIT CIRCLE
AND THESE ARE THE SINE FUNCTION VALUES
WHICH ARE EQUAL TO Y ON THE UNIT CIRCLE.
OKAY, LET'S GO AHEAD AND FINISH BY TAKING A LOOK
AT THE GRAPH OF Y = TANGENT X.
LET'S GO AHEAD AND TURN THESE 2 OFF
AND ENTER TANGENT X AND Y3.
REMEMBER THE RANGE FOR A TANGENT X
IS FROM NEGATIVE INFINITY TO POSITIVE INFINITY,
SO WHEN WE PRESS GRAPH,
THIS GIVES US A DECENT GRAPH OF Y = TANGENT X.
WHAT WE MAY WANT TO DO IS PRESS THE WINDOW KEY
AND CHANGE THE Y MIN AND Y MAX.
LET'S GO AHEAD AND DO THAT.
LET'S CHANGE THE Y MIN TO -5 AND THE Y MAX TO +5.
PRESS GRAPH IT GIVES US THE BETTER PERSPECTIVE
USING THIS WINDOW.
AGAIN IF WE PRESS SECOND GRAPH,
WE SEE THE TANGENT FUNCTION VALUES IN Y3.
REMEMBER TANGENT X IS EQUAL TO SINE X DIVIDED BY A COSINE X.
AND WHEREVER WE SEE AN ERROR,
THIS REPRESENTS WHERE THE TANGENT FUNCTION
WOULD HAVE A VERTICAL ASYMPTOTE.
AND BECAUSE THE PERIOD OF TANGENT X IS 180 DEGREES,
THE NEXT ERROR WILL SHOW AT 270 DEGREES AS WE SEE HERE.
LET'S GO AHEAD AND TURN THE TANGENT FUNCTION OFF,
GO OVER TO THE EQUAL SIGN, PRESS ENTER
AND NOW THEY'RE ALL OFF.
LET'S GO AHEAD AND GRAPH THESE IN RADIAN MODE.
SO FIRST PRESS THE MODE KEY, CHANGE IT TO RADIANS,
PRESS ENTER AND NOW WE HAVE TO ADJUST THE WINDOW
AND THE TABLE SET FOR RADIAN MODE.
SO WE PRESS THE WINDOW,
THE PERIOD FOR COSINE AND SINE DATA IS 2 PI RADIANS.
SO LET'S CHANGE THIS TO -2 SECOND
AND THEN THIS CARAT HERE BRINGS UP THE PI.
WHEN WE PRESS ENTER IT'S GOING TO CONVERT THIS TO A DECIMAL.
AND THEN WE'LL TYPE IN +2 PI FOR THE X MAX.
AND THEN OUR X SCALE -- SCALE IS BY PI/6 RADIANS.
SO LET'S GO AHEAD AND PRESS SECOND CARAT DIVIDED BY 6.
LET'S GO AHEAD AND CHANGE THE Y MIN AND Y MAX BACK TO -2
THROUGH +2.
AND THEN WE ALSO HAVE TO CHANGE OUR TABLE SET,
GOING TO PRESS SECOND WINDOW, START AT 0 RADIANS
AND THEN WE'LL HAVE THE CHANGE
IN THE TABLE PI OVER 6 RADIANS.
AND ONCE WE'VE DONE THIS,
IT'S GOING TO BE PRETTY MUCH THE SAME PROCESS
AS WE SHOWED BEFORE.
LET'S PRESS Y = LET'S GO AHEAD
AND TURN ON THE COSINE FUNCTION,
PRESS ENTER AND GRAPH AND IT LOOKS LIKE JUST WE HAD BEFORE
BUT NOW IT'S GRAPHED IN RADIAN MODE.
IF WE WERE TO PRESS THE TRACE KEY,
NOW X WILL BE IN RADIANS
AND Y WILL BE THE COSINE FUNCTION VALUE.
SO ONE DISADVANTAGE OF RADIANS
IS THAT IT'S SOMETIMES HARD TO INTERPRET
THE ACTUAL ANGLE MEASURE
WHEN IT'S IN DECIMAL FORM AND IN RADIANS.
WE PRESS SECOND GRAPH,
X IS THE RADIAN MEASURE OF THE ANGLE
AND Y1 WOULD BE THE COSINE FUNCTION VALUE.
AND WE COULD DO THE SAME FOR Y = SINE X AND Y = TANGENT X
BUT WE'RE GOING TO GO AHEAD AND STOP HERE FOR THIS VIDEO.
I HOPE YOU FOUND THIS HELPFUL.