Question

I cant solve this can i get some help? 2 cos x + √ 2 = 0

Answer 1

Answer:

Step-by-step explanation:

2 cos x + √ 2 = 0

2 cos x = -√ 2

cos x = -√ 2  / 2

x = arcCos(  -√ 2  / 2 )

so to solve we have to use  "co-terminal " angles .. do you know what I'm saying?  do you understand the words coming out of my mouth :DDDDD OKay back to math and not movie lines .. :P

x = arcCos(  √ 2  / 2 )

x = 45 °

now find the "co terminal" angle that is on 45 ° but in the correct quadrant... since the  -√ 2   is negative.. we now that we go down the y axis.. but also positive on the x axis.. soooo.. that put the angle in the 4th quadrant... so this is an angle of 315° if we go in the CCW  ( counter clock wise )  direction but it's also -45°  in the CW  (clock wise )  direction

below is the table to remember the trig special angles

notice how it's  1,2,3,4    .. so it's super easy to remember.. the trig books don't show you this "trick"   :P

copy and paste this to your computer some where handy

Sin(0) = 0/2      =0  

Sin(30)= $\sqrt{1}$/2   = 1/2  

Sing(45) =$\sqrt{2}$/2 =$\sqrt{2}$/2  

Sin(60)=$\sqrt{3}$/2   = $\sqrt{3}$/2  

Sin(90)=$\sqrt{4}$/2   = 1  

Cos is exactly the same but counts backwards from 90°

Cos(90) = 0/2       = 0

Cos(60) = $\sqrt{1}$ /2   = 1/2

Cos(45) = $\sqrt{2}$/2    =$\sqrt{2}$/2

Cos(30) = $\sqrt{3}$/2   =$\sqrt{3}$/2

Cos(0) = $\sqrt{4}$/2    = 1