![]() That said, the unit circle is not frequently tested, and many of the problems involving the unit circle can be solved through other means (just like most problems on the SAT can be solved in multiple ways). Therefore, there’s a chance that the unit circle will appear on the SAT you end up taking. ![]() Do You Need to Know it for the SAT?Īs one of the main tests used in admissions, the SAT can test on anything covered in high school math classes. Each quadrant follows the patterns described above. Here’s the unit circle you know and love. If we are given radians, we can multiply the value by 360/2π. If we are given degrees, we can multiply it by 2π/360. We can now use the ratio to convert degrees to radians and vice versa. Every other point is correspondingly less than 2π in proportion to the number of degrees the terminal side has moved from the starting position on the right. Thus, 360 degrees corresponds to 2π (or the entire circumference). When it reaches the positive x-axis again, it will have completed a 360 degree rotation. Let’s imagine the terminal side starting at the positive x-axis on the right and rotating about the origin counterclockwise, not unlike the hand of a clock but backwards. The radius is 1, which means that the circumference of the unit circle is 2π. The circumference of the unit circle can be found quickly using the standard circumference formula, which is 2πr. Radians are used to measure the arc of a circle caused by the terminal side (marked in dark green above). Since we now have the measure of Θ (either 30, 45, or 60) we can find the cosine and sine for each of these angles according to the unit circle.īefore we move onto showing the full unit circle, let’s talk about radians. We can now find the sine and cosine for angles equal to 0 or larger than 90.Īlthough this is true for any angle on the unit circle, most math teachers (and the SAT) focus on the points created by the 45-45-90 right triangle and the 30-60-90 triangle (using 30 and 60). In fact, this holds true for any point on the unit circle where you create an angle using a terminal side. ![]() The point (a,b) above can be rewritten as (cos Θ, sin Θ). Sine is opposite over hypotenuse, or b/1. Cosine is adjacent over hypotenuse, or a/1. Using our standard trig definitions above, we can find the cosine and sine of theta. But we can use the above circle to find out the general relationship of a and b to any degree within the circle. The values for a and b depend on the angle in the example above, we’d need to find (or know) the degree from the positive x-axis to the terminal side marked in dark green. These measures are marked a and b respectively. We can then add a line to create a right triangle, where the height is equal to the y-coordinate and the length is equal to the x-coordinate. If we draw a line from the center to a point on the circumference, the length of that line is one (as shown below). Its center is at the origin, and all of the points around the circle are 1 unit away from the center. The unit circle is so named because it has a radius of 1 unit. In some instances, we need to know these values for angles larger than 90, and the unit circle makes that possible. Using these traditional definitions, we are limited to describing the angles we find in right triangles, which are between 0 and 90 degrees. Tangent is the ratio of the length of the opposite leg over the length of the adjacent leg. ![]() Cosine is the ratio of the length of the adjacent leg of the right triangle over the length of hypotenuse.Sine is the ratio of the length of the opposite leg of the right triangle over length of the hypotenuse.If you recall, sine, cosine, and tangent are ratios of a triangle’s sides in relation to a designated angle, generally referred to as theta or Θ. The unit circle is a trigonometric concept that allows mathematicians to extend sine, cosine, and tangent for degrees outside of a traditional right triangle. Will it show up on the SAT, and how will knowing (or not knowing) it affect your score? Read on to find out. You may recall committing the unit circle to memory in your math class, or maybe you’re currently learning it and wondering if you’ll ever see this topic outside a classroom setting. ![]()
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