BRAINLIESTTT ASAP! PLEASE HELP ME :)

θ = 0.896 and 2.246.

Step-by-step explanation:

We will use the identity

sin²θ + cos²θ = 1

and the double angle formula

cos2θ = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ

1. Convert the equation to a more solvable form.

2. Solve the quadratic

a = 2; b = 1; c = -2

(a) Set up the equation.

(b) Evaluate the roots

3. Solve for θ

(a) The negative root

u = sinθ = -1.281

sinθ cannot be less than -1. No solution.

(b) The positive root

If sin(x) = a, then

x = arcsin(x) + 2πn and

x = π - arcsin(a) + 2πn

(i) Case 1

u = sinθ = 0.7808

θ = arcsin(0.7808) + 2πn

θ = 0.8959 ± 2πn

If n = 0,  

θ = 0.8959

(ii) Case 2

θ = π - 0.8959 + 2πn

If n = 0,

θ = π - 0.8959 = 2.246

The solutions are θ = 0.8959 and θ = 2.246

The diagram below shows the graph of f(θ) with its roots at 0.896 and 2.246.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!