Calc 1 test coming up in an hour, in panic mode, can anyone help with how to do this type of problem?

Question

These types of problems are as follows:
sin (arc sin 3 pi / 4)

tan (arc tan 7 pi / 6)

Etc. How can you do these types of problems? I'm really stuck , any help would be greatly appreciated!

Haha I'm not allowed to use a calculator, and am pretty effed. But I think I just found a pattern that might work but still if anyone knows how to do these problems correctly I would greatly appreciate it.

Answer 1

They don't always cancel.

The key is to remember the definitions of the inverse trig functions, INCLUDING their ranges:

arcsin t = the angle between - pi/2 and pi/2 whose sine is t
arctan t = the angle between -pi/2 and pi/2 whose tangent is t

As for your examples:

arcsin 3 pi/4 is an angle whose sine is 3 pi/4. But 3 pi/4 is greater than one, so it is not the sine of anything! Thus there IS no arcsin of 3 pi/4. I suspect you made up this example yourself (which would make you much more devious at exam writing than your instructor is!)

More likely, an exam question might be

sin (arc sin 3/7). Well, arcsin 3/7 is an angle whose sine is equal to 3/7. So the question is "what's the sine of an angle whose sine is 3/7?" The answer is 3/7.

Much trickier is the problem with sin and arcsin in the reverse order:

arcsin (sin 5pi/6) = arcsin ( 1/2) = the angle between - pi/2 and pi/2 whose sine is 1/2 = pi/6.

Answer 2

Use your calculator...calculators have arc options...
Dont know how ur calculator particular works...

change your calculator to radians also to handle the pi...or u gotta conver the pi to degrees

pi = 180 degrees...so pi/4 = 45 degrees, etc...

figure out the arc function on ur calculator...usually its press the ARC function (however it is done), then hit the trig function...

Answer 3

i think that sin would just cancel arcsin and the same with tangent.
if you had a problem where the 2 were different though, you would just need to know the unit circle and if you don't then you better pray that you're allowed to use a calculator.

Answer 4

sin (arc sin (3* pi / 4))= 3 *pi/4, the sin and arc sin cancel,
sin*sin^1=sin/sin=1

etc.

Answer 5

lol you're ******. go google it.