6.2 Verifying Identities Graphically

Graphing Crash Course!

Put calculator in Radian Mode MODE  3 rd one down RADIAN (select) 2 nd MODE to Quit You enter equations by selecting Y = (1 st top button) Let’s graph basic

y

= sin

x

&

y

= sec

x

for practice Y 1 = sin(x) to get x, use X, T, θ, n button Y 2 = 1/cos(x) toggle over to left side of Y 2 , hit ENTER until it changes to -0 ZOOM  7: Ztrig We will use our graphing calculators to decide if an equation appears to be an identity.

(Remember, this is not a proof!)

For all examples, use your graphing calculator to determine whether each example appears to be an identity.

- Remember to -0 graph the second one!

- Anytime you see a variable ( , , θ, etc), you type X Ex 1) cot   cos  sin  Y 1 Y 2 = 1 / tan(x) = cos(x) / sin(x) Yes Ex 2) csc( )  sec  Y 1 Y 2 = 1 / sin(x – π) = 1 / cos(x) No

Ex 3) sin  tan csc     cot  Y 1 Y 2 = (sin(x)*(1 /sin(x))) / tan(x) = –1 / tan(x) No Ex 4) sec 2   tan 2  2 cos 2  Y 1 Y 2 = (1 / cos(x)) 2 = 2 / cos(x) 2 + tan(x) 2 + 1 Yes

Ex 5) cos cos

x



x

sin

x

 cot

x x

Y 1 Y 2 = cos(x) / (cos(x) + sin(x)) = (1 / tan(x)) / (1 + (1 / tan(x))) Yes Ex 6) Sin  1

x

 Cos  1

x

  2 Y 1 Y 2 = sin –1 (x) = cos –1 (x) + π/2 No

Homework #605 Pg 294 #1, 5, 9, 11, 12, 17, 25, 29, 34, 35, 38, 39, 41, 43, 46

Even Answers: #12: Yes #34: No #38: 8; 1/40; 40 #46: No