Solve for x in the given interval.

sec θ = -4.0545, for 0≤θ≤2π

The answer is Ф = 1.82 or 4.46 ⇒ answer (c)

Step-by-step explanation:

* The domain of the function is 0 ≤ Ф ≤ 2π

- Lets revise the ASTC rule to solve the problem

# In the 1st quadrant all trigonometry functions are +ve

# In the 2nd quadrant sinФ and cscФ only are +ve

# In the 3nd quadrant tanФ and cotФ only are +ve

# In the 4th quadrant cosФ and secФ only are +ve

* Lets solve the problem

∵ secФ = -4.0545 ⇒ negative value

∴ Angle Ф is in the 2nd or 3rd quadrant

- In the 2nd quadrant Ф = π - α ⇒ (1)

- In the 3rd quadrant Ф = π + α ⇒ (2)

where α is an acute angle

* Now use the calculator to find α with radiant mode

- Let secα = 4.0545

∴ cosα = 1/4.0545

∴ α = cos^-1(1/4.0545) = 1.321585

* Substitute the value of α in (1) and (2)

∴ Ф = π - 1.321585 = 1.82

∴ Ф = π + 1.321585 = 4.46

* The answer is Ф = 1.82 or 4.46