Find all exact solutions on the interval. If there more than one answer, enter them as a comma separated list.

Question

Find all exact solutions on the interval 0 ≤x<2pi

1: cot(𝑥)+1=0

2: 4sin²(𝑥)−3=0

3: csc²(𝑥)−2=0

2sin(3𝜃)=√(2)

Need help with these 4 different question please and thank you.

Answer 1

1) cot(𝑥) + 1 = 0 or cot(𝑥) = -1 Using the unit circle, you can see this occurs at 3π/4 and 7π/4

2) 4sin²(𝑥) − 3 = 0 or:

4sin²(𝑥) = 3 or:

sin²(𝑥) = 3/4 or

sin(𝑥) = ±√(3/4) or

sin(𝑥) = ±√3/2

Using the unit circle, you can see this occurs at π/3, 2π/3, 4π/3, and 5π/3

For the other problems, keep doing just like this. remember that csc²(x) = 1/sin²(x)