Find all angles in degrees that satisfy each question.
2sin(a)+rad2=0
To find all angles in degrees that satisfy the equation 2sin(a) + √2 = 0, we can start by isolating the sin(a) term.
1. Subtract √2 from both sides of the equation:
2sin(a) = -√2
2. Divide both sides of the equation by 2:
sin(a) = -√2/2
Now, we need to find the angles in degrees whose sine is equal to -√2/2. To do that, we can use the inverse sine function or the unit circle.
1. Using the inverse sine function:
Let's calculate the inverse sine of -√2/2:
a = sin^(-1)(-√2/2)
Using a scientific calculator or a trigonometric table, find the angle whose sine is -√2/2. The result for a will depend on the calculator's settings, but typically, you will get a value of -45° or 315°.
Therefore, the angles that satisfy the equation 2sin(a) + √2 = 0 are -45° and 315°.
2. Using the unit circle:
On the unit circle, the sine function gives the y-coordinate of a point on the unit circle. For an angle in standard position (starting from the positive x-axis), we look for the angles where the y-coordinate is -√2/2. These angles are 45° (or 225°) and 315°.
Therefore, the angles that satisfy the equation 2sin(a) + √2 = 0 in degrees are 45° (or 225°) and 315°.