# Find all exact angles x in the interval [0,360°] that satisfy the following equations without the use of calculator a)sin x +cos 2x=0 b)cos 2x= sin52 ?

##### 1 Answer

Aug 30, 2015

Solve sin x + cos 2x = 0

Ans:

#### Explanation:

Replace in the equation

Since (a + b + c = 0), use the shortcut. The 2 real roots are:

a. sin x = 1 -->

b.

Ans:

Check by calculator.

x = 90 -> sin x = 1, cos 2x = cos 180 = -1 --> 1 - 1 = 0. OK

x = (7pi/6) = 210 -> sin x = -0.5; cos 2x = cos 420 = cos 60 = 0.5 ->

Therefor, -0.5 + 0.5 = 0. OK

x = (11pi)/6 -> sin 330 = -0.5; cos 660 = cos 300 = 0.5.

Therefor, -0.5 + 0.5 = 0. OK