4.7 Flashcards
trig(arctrig(x))
put in ratio, get out ratio
arctrig(trig(x))
put in angle, get out angle.
How many solutions do evaluate problems have?
one angle or ratio, because to get an angle for a solution the final bracket must be an arctrig
How are evaluate problems constructed
cos(arctan(rt.3)= (nothing– just have to solve for one solution)
What must you remember when the arctrig is on the outside, so you are solving for an angle?
Domain restrictions of inverse functions.
How could you solve the problem: sec(arcsin(3/5)), because 3/5 is not a ratio you are familiar with?
You know that the answer will be a ratio, also, so you don’t have to worry about solving for the angle. Construct a triangle for the angle which the inner function represents
So, when do you construct a triangle for evaluate problems?
when arctrig is on the inside.
Simplify has what?
x-variables– you may have to construct a triangle using x-variables with unsimplifiable square roots. These ones always have had arctrig on the inside.
Solve equations have what type of solution?
0-2 solutions (2 can mean two equations for angle)
How are simplify problems written?
trig(arctrig(x/n)). They are not equal to anything.
How are solve equations written?
arctrig(trig(x)) or opposite. Careful, there are specific solving rules here.
In what scenario can you take the trig of the other side?
in a solve, where it is constructed arctrig(trig(x))=angle. If you take the arctrig of the angle in the equation trig(arctrig(x)), you will cause domain restrictions. In this scenario, you work from the inside out, calling the inside just an angle and solving from there.
still need to add: graphs. Make sure I understand.
there is a half-circle one…
When the arctrig is on the outside of the graph, what is the domain of the graph.
Infinite.
