Question

Question 37 the answer is about x=5.25 can someone please explain to me how to do that problem without a calculator also question 39 there is supposed to be two answers I found .52 but the other one is x=2.26 and idk how to get that one and again no calculator

Answer 1

37) m∠x = 5.25

39) m∠x = 0.5236 and m∠x = 2.62

Explanation:

37)

∵ cotx = -0.6 and 3π/2 ≤ x ≤ 2π

∴ tanx = -1/0.6

∵ ∠ x in the fourth quadrant ⇒ ∴ m∠x = 2π - α where α is an acute angle

∵ tanα = 1/0.6 ⇒ α =
`tan^(-1)(1)/(0.6)`

∴ α = 1.03038

∴ m∠x = 2π - 1.03038 = 5.25

39)

∵ cscx = 2 and 0 ≤ x ≤ 2π

∴ sinx = 1/2 ⇒ +ve value

∴ ∠x is in the first quadrant or the second quadrant

∴ m∠x = α or m∠x = π - α

∵ sinα = 1/2 ⇒ ∴ α =
`sin^(-1)(1)/(2)`

∴ α = 0.5236

∴ m∠x = 0.5236

∴ m∠x = π - 0.5236 = 2.6216 ≅ 2.62