1. ## Finding Solutions

I'm having trouble on these last questions. Help would much appreciated.

1. Find all solutions of the equation. (Enter each answer in the form θ + 2πk, 0 ≤ θ < 2π.

2. Consider the equation.

(a) Use an addition or subtraction formula to simplify the equation.
(b) Find all solutions in the interval [0, 2π).

3. As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phases of the moon describe how much of the surface appears to be in sunlight. An astronomical measure of phase is given by the fraction F of the lunar disc that is lit. When the angle between the sun, earth, and moon is θ (0 ≤ θ < 360°), then the fraction F is given by the formula below. Determine the angles θ that correspond to the following phases. (If there are any unused answer boxes, enter NONE in the last boxes.)

(b) F = 0.25 (crescent moon)
(c) F = 0.5 (first or last quarter)
(d) F = 1 (full moon)

I tried putting it in the calculator and it didn't work I put it both radians and degrees. I put it the calculator like this (1/2)(1-cos(x))

2. Originally Posted by goldenroll
I'm having trouble on these last questions. Help would much appreciated.

1. Find all solutions of the equation. (Enter each answer in the form θ + 2πk, 0 ≤ θ < 2π. ... equation?

2. Consider the equation.

use the difference identity sin(a-b) = sin(a)cos(b)-cos(a)sin(b)

(a) Use an addition or subtraction formula to simplify the equation.
(b) Find all solutions in the interval [0, 2π).

3. As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phases of the moon describe how much of the surface appears to be in sunlight. An astronomical measure of phase is given by the fraction F of the lunar disc that is lit. When the angle between the sun, earth, and moon is θ (0 ≤ θ < 360°), then the fraction F is given by the formula below. Determine the angles θ that correspond to the following phases. (If there are any unused answer boxes, enter NONE in the last boxes.)

(b) F = 0.25 (crescent moon)
(c) F = 0.5 (first or last quarter)
(d) F = 1 (full moon)

(a) F = 1/4 ... [1 - cos(t)] = 1/2 ... cos(t) = 1/2 ... t = 60 , t = 300

(b) F = 1/2 ... [1 - cos(t)] = 1 ... cos(t) = 0 ... t = ? (two solutions)

(c) can you do this one now?
.