Use the given information to find the cos (2,0), csc q = 5/3, q lies in n quadrant II
How would I go about doing this
What does this symbolism mean?
Cos(2,0)
Then: cos(2,0),csc q what kind of math symbol is that?
cosine ( x,y) csc(theta,or angle)I don't have a theta symbol om my keyboard and they use that interchangable in my book
The problem I have is not q, but the (x,y) as an angle.
oh ok sorry I'll try to be more specific
I don't know what I mean I'm very confused , just disregard intil I cn puit more info in there
To find the value of cos(q), where q lies in Quadrant II and csc(q) is given, we can use the following identities:
1. csc(q) = 1/sin(q)
2. sin^2(q) + cos^2(q) = 1
Given that csc(q) = 5/3, we can find sin(q) as follows:
csc(q) = 1/sin(q)
5/3 = 1/sin(q)
We can solve this equation for sin(q) by cross-multiplying:
3 = 5sin(q)
sin(q) = 3/5
Since q lies in Quadrant II, sin(q) is positive, but cos(q) is negative. Using the Pythagorean identity sin^2(q) + cos^2(q) = 1, we can find cos(q) as follows:
sin^2(q) + cos^2(q) = 1
(3/5)^2 + cos^2(q) = 1
9/25 + cos^2(q) = 1
cos^2(q) = 1 - 9/25
cos^2(q) = 16/25
Taking the square root of both sides:
cos(q) = ±√(16/25)
Since q lies in Quadrant II where cos(q) is negative, the final answer is:
cos(q) = -√(16/25)
cos(q) = -4/5
Therefore, cos(q) is equal to -4/5.