Question

Find all values of theta where 0degrees<theta<360 degrees when csc theta = square root 2

Please detail how/why i can get to the solution. I need to understand the concept clearly...... It will probably relate to something taught down the line I'm sure.

Answer 1

see prior post. and geez, wait a bit willya?

Answer 2

given : cscØ = √2

or by definition: sinØ = 1/√2

recall the CAST rule, which says that the sine is positive in quadrants I or II

method 1: recognize the main trig ratios of 0°,30°, 60°, 45°, 90°
we know that sin 45° = 1/√2
so Ø is 45 in quadrant I
or
Ø is 180-45 or 35° in quadrant II

method 2: (if you don't know the main rations)
have your calculator find 1/√2 = .7071...
make sure it is set to degrees,
press 2ndF sin, then =
to get 45

If you are doing a lot of these angle related problems, I suggest you copy in your notebook pictures of the 30-60-90 and the 45-45-90 degree triangles with the ratio of their sides:
1 : √3 : 2 for the first and 1 : 1 : √2 for the second
(notice how I recognized the 1/√2 from the last part ? )

Answer 3

Steve , did not realize you had already given a detailed explanation.
Patience would have indeed been a virtue that could have been exercised by the poster.

Answer 4

Thank you to both of you, I am new to this site and it has been a blessing. Reiny your CAST rule which I was not taught, is very helpful. Your whole post will be useful come my exam. My book is not as straight forward..I fear for my GPA. :(