Determine the measure of A if 0 degrees is less or equal to angle A and if angle A is less or equal to 360 degrees.
Tan A = 0
Answer is somehow supposed to be 0 degrees, 180 degrees, and 360 degrees, but don't know how to get the answer, just really confused.
Sin A = -1
In your text you should have the graphs of the
sine, cosine and tangent curves.
Take a look where the tangent curve cuts the x-axis in the given domain
for the second, look at the sine curve,
when is it at -1, its lowest value.
To determine the measure of angle A when tan A = 0, we need to find the values of A that make the tangent of A equal to 0.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. The tangent of an angle is 0 when the side opposite the angle is 0. In other words, when the side opposite the angle has a length of 0, the tangent of that angle is 0.
Now, let's think about the unit circle, which is a circle centered at the origin (0,0) with a radius of 1. The angle A can be represented by a point on the unit circle. The x-coordinate of that point represents the cosine of angle A, and the y-coordinate represents the sine of angle A.
Since the tangent is the sine divided by the cosine, when the tangent is 0, the sine must also be 0. Therefore, angle A must be one of the angles where the sine is 0.
The sine of an angle is 0 at three angles on the unit circle: 0 degrees, 180 degrees, and 360 degrees. These angles are the x-axis intercepts of the unit circle, where the y-coordinate is 0.
So, the possible measures of angle A, when tan A = 0, are 0 degrees, 180 degrees, and 360 degrees.
Now, let's consider the second question where sin A = -1. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The sine of an angle can range from -1 to +1. When the sine is -1, it means that the angle is the maximum negative value.
In the unit circle, the sine is -1 at the angle of 270 degrees or -90 degrees. These angles are the y-axis intercepts of the unit circle, where the x-coordinate is 0.
Therefore, the measure of angle A, when sin A = -1, is either 270 degrees or -90 degrees.
Remember to consider the given conditions and the unit circle to determine the possible measures of angles.