Trig help...exam tomorrow?

Question

i asked a question like this earlier only this time its

Sin^-1 (-1/2)

how would you go about solving this? what does the negative attached to the sine mean? Thanks in advance

thanks a lot guys you've been a big help, but what about something like tan^-1(tan2pi/3)

the answer on the review sheet says -pi/3. but i dont see how he got it

Answer 1

it means inverse sin. What this is asking is what number, when you take the sin of it, will give you -1/2. Since when you take the sin of 30 degrees, the answer is 1/2, then you know that the sin of -30 degrees (also known as 360-30 *330 degrees*) will give you a negative one half.
If you have a nicer calculator, you should have a sin^-1 button. To get the answer, hit the button and plug in -.5. It will give you -30.
Make sure your calculator set on degrees by hitting sin(30). IF it gives you .5, your ready to go.

Answer 2

First, you don't need the carat after the Sin.
This is an inverse statement; that is what the -1 is all about.
.The original statement was Sin (x) = -1/2, this statement is the inverse, and would be stated as
"the sin of what angle is -1/2." To solve, you would go to your trusty calculator or trig table and find the angle at which the sine is -0.5. Since the sine function is periodic, in the interval (0, 2pi), this happens at 2pi/3 and 11pi/6

Answer 3

for the sin function to be negative, it is either on 3rd or 4th quadrant
we all know sin30 degree is 1/2
therefore the solutionis 150+360k,330+360k where k is any integer

Answer 4

means the sine function is in a quadrant in which it is negative. remember the A C T S rule

Answer 5

the sec of pi/3 could be 2 b/c your cos of pi/3=one million/2 and your sec is the inverse of that so 2 is your answer. Unit circles do wonders! :) Csc of 690 stages could be -2 b/c your sin of 690 stages is -one million/2 and csc is inverse of sin so -2......

Answer 6

sin^--1(--1/2)
= sin^--1{sin(--pi/6)}
= npi + (--1)^n (-- pi/6)