![]() Getting back to this specific question, since, and have to be the two smaller angles of the right triangle. Well, in a right triangle, when you switch from one of the smaller angles to the other one, you are swapping which side is Opposite and which side is Adjacent! (The Hypotenuse always remains the same side.) Based on SOH and CAH, swapping the Opposite and Adjacent sides means the same thing as swapping the sine and cosine values of the angles. If you understand SOH-CAH-TOA and right triangles, this is logical: From SOH and CAH, you can see that the only difference between the sine and the cosine is that the sine has the Opposite side length in the numerator and the cosine has the Adjacent side length in the numerator. The cosine of one angle = the sine of the other angle. The sine of one angle = the cosine of the other angle. In a right triangle, there are always two smaller angles. ![]() Here is another way to think about these rules: ![]() You must know these rules to be able to solve advanced SAT trigonometry questions! The next piece of advanced knowledge about trigonometry that the SAT loves to test is the following set of rules: You probably know SOH-CAH-TOA for sine, cosine, and tangent, which of course is absolutely necessary knowledge for the trigonometry questions on the SAT.
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