Question

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

Answer 1

oh well. Clearly you aren't going to try.

45 and 135

Answer 2

I don't want just the answer but how to get to it. I need to fully understand how to arrive at the conclusion....And that is clearly where I am struggling.

Answer 3

Can you please detail why that is the answer?

Answer 4

review your basic angles. They are

0,30,45,60,90 in QI.

the values for 45 are
sin=1/√2
cos=1/√2
tan = cot = 1
csc=√2
sec=√2

This is because for 45 degrees, the sides of the right triangle in the ratio 1:1:√2

The 30-60-90 triangle has sides 1,√3,2, so you can figure the functions there.

If the angle is drawn in standard position (with the base along the x-axis, with one corner at the origin), then

sin = y/r
cos = x/r
tan = y/x
etc.

r is the hypotenuse, so it is always positive.

Since y is positive in QI and QII, so are sin and csc.

I'm sure this is all explained in greater detail, with examples, in your text.