Question

Solve the trigonometric equation for the angle x between 0 degree to 360 degrees.cosx =15

Answer 1

The given trigonometric equation is

`\cos x=(1)/(5)`

Notice that the cos function is positive

Using the idea of the quadrant, notice that cosine is positive in the first and fourth quadrants.

The value of x in the first quadrant is:

`\begin{gathered} x=\cos^(-1)((1)/(5)) \\ x=78.5^(\circ) \end{gathered}`

Therefore the value of x in the first quadrant is 78.5 degrees.

The value of x in the fourth quadrant is

`\begin{gathered} 360-x \\ =360-78.5 \\ =281.5 \end{gathered}`

Therefore the value of x in the fourth quadrant is 281.5 degrees.