Big Question Blog Post #1

How do the trig graphs relate to the Unit Circle?

The trig graphs relate to the unit circle because when we graph a trig function, we are basically taking the unit circle and stretching it into a line. We also need to look at ASTC to know how the trig graphs relate to the unit circle. Sine's pattern is positive, positive, negative, negative. That means that in the first two quadrants sine is positive and in the next two quadrants, sine is negative. When we graph sine, the first two sections are above the x-axis because they are positive. The next two sections of the sine graph are below the x-axis because sine is negative in quadrants three and four. In the picture below, we see how the sine graph relates  to the unit circle because we know that the sine of 90 is one and that is shown on the graph. The cosine and tangent graphs also relate to the unit circle based on the pattern they have. For example, cosine's pattern is positive, negative, negative, positive. Tangent's pattern is positive, negative, positive, negative. 

a. Period: The period for sine and cosine is 2 pi and the period of tangent and cotangent is pi. The period for sine is 2 pi because the pattern for sine and cosine takes two periods to to repeat. The pattern for sine is + + - - and the period for cosine is + - - +. The period for sine and cosine because their respective patterns take two periods to repeat. The period for tangent and cotangent is only one period long because the pattern only takes one period to repeat itself. The pattern for tangent is + - + -.

b. Amplitude: Amplitude is the distance between the lowest point and the highest point on the graph. We know that sine and cosine have amplitudes because of the values on the unit circle. Tangent and cotangent don't have amplitudes because those graphs go uphill and downhill. Since these graphs go uphill and downhill, it is not necessary to have an amplitude.