Question

Solve the equation (Picture provided)

Answer 1

The solutions of the equation are 120° , 240° ⇒ 4th answer

Explanation:

* Lets revise how to solve the trigonometry equation

- At first Look to the domain

- Use the ASTC rule to know the quadrants of the angle x

# A ⇒ in the 1st quadrant all trigonometry functions are positive

# S ⇒ in the 2nd quadrant sin only is positive

# T ⇒ in the 3rd quadrant tan only is positive

# T ⇒ in the 4th quadrant cos only is positive

- Use the calculator to find the acute angle α which has the positive

value of the trigonometry function of x

# In 1st quadrant x = α

# In 2nd quadrant x = 180° - α

# In 3rd quadrant x = 180° + α

# In 4th quadrant x = 360° - α

* Now lets solve the problem

∵ The domain is 0° ≤ x ≤ 360°

∵ cos x = -1/2

- The value of cos x is negative

∴ ∠x is in the 2nd or 3rd quadrants ⇒ according to ASTC rule

- Lets find the acute angle α, where cos α = 1/2

∵ cos α = 1/2

∴ α = 60°

∵ ∠x lies in the 2nd quadrant

∴ x = 180° - α = 180° - 60° = 120°

∵ ∠x lies in the 3rd quadrant

∴ x = 180° + α = 180° + 60° = 240°

* The solutions of the equation are 120° , 240°

Answer 2

The correct answer option is D. 120°, 240°.

Explanation:

We are given the information about x that
`cos x=-(1)/(2)`.

We know that [tex]cos x=-\frac{1}{2}[/tex ] is actually the ratio of adjacent side to the hypotenuse. It means that here, adjacent is -1 and hypotenuse is 2.

A negative cosine tells us that the angle is either in Quadrant II or Quadrant III.

So if it is in 2nd quadrant, then x = 120° and if its in 3rd quadrant then x = 240°.