Question

17. Sketch the graph of the following tangent and secant functions. a.y=tan(3x - 1/2) b.y = 3 sec(2x - 1/2) 18. trig and inverse trig Braph of region of y = sin from xto x=t, observe this is one to one and thus has an verse. Then use the principle of reflection about vax to find the graph of this inverse. b. Repeat the same for y = cos x from x= -1/2 to x=7t/2.

Please help me solve these 2 questions with steps. Thank you.

Answer 1

am (a) The giren tangent fumetion is y = tam (3x - 11/2) Simee the period of tim a is T them the girem finetion had period 1/3

. We tabulate y between - Uz to 4/3 with Step size o X -U-WA-W/6-W12 o 17/12 W/64 TA Now we Sketch the function MI -W/3 low 7-116W 1073

11/8 -31/8 -21/8/-/8 To TT/8 21/8

O2 03 03 (6) the given function y = 3 See ( 22 - 11/2) since the period I see a is zu Then the given fumetion hang per fabulate y between the to 1/2 with step win SUNDAY 16 04

Now we Sketch the function -

-W) AA

40 -T -1/2 1/2

(10@we Sketch ya sima from o We is observe that the finetion one to one im between a so to na 1/2

231-13 27 28 29 Now we fake reflection about y = x line and get the inverse of the fimetion

0.5 2. о. п/4 2п/4 Зг/4 Х -0.5

6 we y = dor Sketch the function Cada from 2241/2 to xzub We obserne that y is one to om in between 2-0 box-1/2 Now we take reflexion reflextion about the line yox and get of the group of the inverse of the fimetion

у 2.0 1.5 0.5 п/4 -п/4 п/4 23/4 Зл х |-0.5