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