oh well. Clearly you aren't going to try.
45 and 135
Find all values of theta where 0degrees<theta<360 degrees when csc theta = square root 2
4 answers
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.
Can you please detail why that is the answer?
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.
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.
1 answer