Answer:
See below for answers and explanations to the first 5 problems
Explanation:
Problem 1:
cos(x) = 2/3
sec(x) = ?
sec(x) = 1/cos(x)
sec(x) = 1/(2/3)
sec(x) = 3/2
Problem 2:
sinβ = -5/6
cscβ = ?
cscβ = 1/sinβ
cscβ = 1/(-5/6)
cscβ = -6/5
Problem 3:
secφ = 2
tanφ = √3
sinφ = ?
secφ = 1/cosφ
tanφ = sinφ/cosφ
tanφ = sinφ/cosφ
tanφ = sinφ(1/secφ)
√3 = sinφ(1/2)
2√3 = sinφ
Problem 4:
secθ = 8
tanθ = 3√7
cscθ = ?
secθ = 1/cosθ
tanθ = sinθ/cosθ
cscθ = 1/sinθ
tanθ = sinθ/cosθ
tanθ = sinθ(1/cosθ)
3√7 = sinθsecθ
3√7 = sinθ(8)
(3√7)/8 = sinθ
cscθ = 1/sinθ
cscθ = 1/((3√7)/8)
cscθ = 8/(3√7)
cscθ = (8√7)/21
Problem 5:
sinθ = 2/√5
cosθ = 1/√5
tanθ = ?
tanθ = sinθ/cosθ
tanθ = (2/√5)/(1/√5)
tanθ = (2/√5)(√5)
tanθ = 2