Question

General Solutions: Pre-calc/Trig

Can someone explain the picture below? I don't understand how they went from step 3 to step 4. But I understand a general solution is y=___?___ +2pi(K)

Answer 1

I also know why it is x=, because we were solving for x in step 3

Answer 2

I don't understand how they went from step 3 to step 4.

which step is that ?

Answer 3

Like.. I don't understand how they went from solve sinx=1/2 to x=30degrees+/- 2pi(K)
How did they know that it would be 30?

Answer 4

In general, you use a calculator.

The question is (apparently) what is the inverse sin (or arc sine) of 1/2 ?
or, "what angle is it that the sin of that angle = 1/2 ?"

in google's search wind, type
asin(1/2) in degrees=

or use a calculator.

however, people memorize a few important angles:
sin(0) = 0
sin(30º) = 1/2
sin(45º)= sqrt(2)/2
sin(60º) = sqrt(3)/2
sin(90º)= 1

Answer 5

Oh okay. When you type it into a calculator will it give you the degrees?

Answer 6

Oh I see now. I just had to put it in degree mode.

Answer 7

In the days before computers, they had tables with the values of sin , cos , tangent.
now we can use a calculator.

When you type it into a calculator.. Did you try?

Answer 8

yes, in degree mode you get degrees, radian mode, you get radians
if you get weird numbers, always check your mode.

Answer 9

Okay, thanks :) I have a question, a specific example. Can you help me real quick?

Answer 10

But on a test they may expect you to memorize the angles I posted up above.

Answer 11

Ok , what is the question?

Answer 12

Write the general solution to y = arcsin (0.6428).
When I put it in my calculator, I put in sin^-1(0.6438). I got roughly 40degrees. How do I find the other answer of 140? I know they are both right (40 &140) but I don't know how to find them both. Does that make sense?

Answer 13

yes

here is a graph of sin: