Question

Solve each trigonometric equation such that 0 ≤ xx ≤ 2????????. Give answers in exact form.

a. √2cos(x) + 1 = 0
b. tan(x) − √3 = 0
c. sin2(x) − 1 = 0

Answer 1

Answer: a) 120° b) 60° c) 45°

Explanation:

a) a. √2cos(x) + 1 = 0

We need to make 'x' the subject of the formula first

√2cos(x) = 0-1

√2cos(x) = -1

Cos(x) = -1/√2

x = arccos(-1/2)

x = -60°

Since cosine is negative in second and third quadrant, X = 180-60 = 120° (2nd quadrant)

X = 180+60 = 240°(3rd quadrant)

We will go for x= 120° being the lesser value.

b) tan(x) - √3 = 0

tan(x) = √3

x = arctan√3

x = 60°

c) sin2x-1 =0

Sin2x = 1

2x = arcsin1

2x = 90°

x = 90°/2

x = 45°