Trig/Inverse Trig Functions - Unit 4 HPreCalc

What critical points make up the cosine asymptotes

1st, 3rd , and 5th.

• parent function w/period 2pi would hv asymptotes at 0, pi, and 2pi

• min/max at 1/2pi and 3/2pi

What critical points make up the sec asymptotes

2nd and 4th

• Pi/2 and 3pi/2 on parent graph.

• 0, pi, 2pi would be max min max. Follow the cos max min max

what critical points on a tangent function make up the asymptotes

Middle of a cycle (pi/2)

• tangent takes on a increasing cubic form. A cycle is the top half of a cubic, asymptote, bottom then top again, and so on.

• Period is pi

what critical points on a cot function make up the asymptotes

start and end of a cycle

• Function is flipped, looks like a decreasing Cubic. Cubic origin in middle of cycle, at pi/2

• Period of pi

What let’s functions have inverses?

Must be 1-1 (NO EVEN) pass horizontal and vertical line test.

• Symmetrical about line y = x

Domain and ranges of inverse functions

• sin w/ Q4, Q1 ; [-pi/2, pi/2] range for angle, and [-1, 1] domain for trig value

• Cos w/ Q1, Q2 ; [0, pi] range for angle, and [-1, 1] domain for trig value

• Tan w/ Q4, Q1 ; (-pi/2, pi/2) {excluded bc asymptotes} range for angle, and all real numbers domain for trig value

Inverse trig function purpose:

Used to find the OG angle.

Example:

• -rt3/2 could work with Q3, or Q4. But arcsin only works with Q1, Q4, so it would be in Q4

• However, this exceeds the pi/2 domain, so must be rewritten as -pi/3 instead of 5pi/3

Evaluating sin of arccos etc

• if taking trig of an inverse, get the angle first. Then do as usual.

• If you wanna cancel, first adjust the angle to fit the domain, then cancel

• Some angles cannot fit domains, like pi into cos (REVIECTHIS 8 On day 2 NOTES)