Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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:

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

simplify square:

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

reduce fraction:

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

simplify substraction and hence,

$\rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}$