Solve for x in the given interval.sec θ = -4.0545, for 0≤θ≤2π

Answer: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