Question

Cos 600 degrees solved by double angle formula (20 points)
show work please :)))

Answer 1

`\rm\cos({600}^( \circ) ) =-1/2`

Explanation:

we would like to solve the following using double-angle formula:

`\displaystyle \cos( {600}^( \circ) )`

there're 4 double Angle formulas of cos function which are given by:

`\displaystyle \cos(2 \theta) = \begin{cases} i)\cos^(2) ( \theta) - { \sin}^(2)( \theta) \\ii) 2 { \cos}^(2)( \theta) - 1 \\iii) 1 - { \sin}^(2) \theta \\ iv)\frac{1 - { \tan}^(2) \theta}{1 + { \tan}^(2) \theta } \end{cases}`

since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore

step-1: assign variables

to do so rewrite the given function:

`\displaystyle \cos( {2(300)}^( \circ) )`

so,

• 
  `\theta = {300}^( \circ)`

Step-2: substitute:

`\rm\cos(2 \cdot {300}^( \circ) ) = 2 \cos ^(2) {300}^( \circ) - 1`

recall unit circle thus cos300 is ½:

`\rm\cos(2 \cdot {300}^( \circ) ) = 2 \left( (1)/(2) \right)^2 - 1`

simplify square:

`\rm\cos(2 \cdot {300}^( \circ) ) = 2\cdot (1)/(4) - 1`

reduce fraction:

`\rm\cos(2 \cdot {300}^( \circ) ) = (1)/(2) - 1`

simplify substraction and hence,

`\rm\cos({600}^( \circ) ) = \boxed{-(1)/(2)}`