Trig Identities in Equations Brought to you by Seamus and Lucas

What are the Trig Identities?

Problem 1 Solve for all values of x when 0°≤x<360°:

Solution 1 cos -1 (½)= x x= 60° x= 300° cos -1 (1)= x x= 0°

Problem 2

Solution 2

Problem 3 Find, to the nearest degree, all values of X between 0° and 360° that satisfy the equation 2sinx + 4cos2x=3

Solution 3 2sin(x) + 4(1-2sin 2 x) - 3=0. 2sin(x) sin 2 x - 3=0 -8sin 2 x + 2sin(x) + 1=0. {30°, 150°, 346°, 194°} -8sin 2 x + 4sin(x) - 2sin(x) + 1=0 4sin(x)(-2sin x +1) 1(-2sin x + 1) -2sin(x) + 1=0. 4sin(x) + 1=0 x=sin -1 (½). x=sin -1 (-¼) 30°. -14° (reject) 150°. 346° 194°