SOLVING TRIGONOMETRIC EQUATIONS AND FINDING TRIGONOMETRIC VALUES BASED ON GIVEN INFORMATION.

Question

Find all x, such that 0 ≤ x ≤ 2π

1) tan(x) = -1

2) 2cos(x) - 1 = 0

3) sin(2x) = 2cos(x)

Answer 1

James

Create a trig table

x 0 pi/6 pi/4 pi/3 pi/2

cos 1 √3/2 √2/2 1/2 0

sin 0 1/2 √2/2 √3/2 1

tan. 0 √3/3 1 √3 DNE

tan(x) = -1 means x =pi-(pi/4) = 3pi/4. or x=2pi-pi/4 = 7pi/4

2cos(x)-1 = 0 means 2cos(x) = 1. so. cos(x) = 1/2. This is true for pi/3 and for 2pi-(pi/3) = (5pi)/3.

Try to figure out the last one