help its due in 1 hour! precalculus

Question

If , and  is in quadrant II , then find

(a)    

(b)    

(c)    

(d)    

(e)    

Answer 1

We are told sin(θ)=2/3, and we know that sin is opposite over hypotenuse. So we know two sides of the triangle, and can calculate the third side.

opposite² + adjacent² = hypotenuse²

2² + adjacent² = 3²

adjacent² = 9 - 4

adjacent = √5

Now since we have all the sides (o = 2, h = 3, a = √5), we can answer the other parts.

(a) cos(θ)=   a / h = √5 / 3

(b) tan(θ)=   o / a = 2 /√5

(c) sec(θ)=   h / a = 3 / 2

(d) csc(θ)=   h / o = 3 / 2

(e) cot(θ)=   a / o = √5 / 2

Hope this helps!

Answer 2

sinx = 2/3 in quadrant II

sine is opposite/hypotenuse = o/h = 2/3, o=2, h=3

cosine is adjacent side/hypotenuse = a/h = a/3, where a^2 = h^2-o^2 = 9-4=5

a = sqr5

cosx= -sqr5/3

cscx = 1/sinx = 3/2

secx = 1/cosx = -3/sqr5

tanx = o/a = -2/sqr5

cotx =a/o = -sqr5/2