![]() ![]() The ratios sin, cos, tan, sec, csc, and cot will be the same for angle θ, no matter the length of the sides of the triangle. Therefore, if one right triangle has an angle that measures θ, it will be similar to another right triangle that measures θ. These relationships can be determined from the Pythagorean Theorem.Īll right triangles, regardless of size, are similar if they have angles that measure the same. The inverse of tangent is the cotangent, and the cotangent of θ (cot θ) is the ratio of the adjacent side to the opposite side. The inverse of cosine is the cosecant, and the cosecant of θ (csc θ) is the ratio of the hypotenuse to the adjacent side. The inverse of sine is the secant, and the secant of θ (sec θ) is the ratio of the hypotenuse to the opposite side. There are three other trigonometric ratios that are the inverses of sine, cosine, and tangent. Those three ratios can be measured by the mnemonic SOHCAHTOA. The sine of θ (sin θ) is the ratio of the opposite side to the hypotenuse, the cosine of θ (cos θ) is the ratio of the adjacent side to the hypotenuse, and the tangent of θ (tan θ) is the ratio of the opposite side to the adjacent side. ![]() Suppose a right triangle has an angle θ for one of the acute angles. Those ratios reflect the relationships between the opposite and adjacent angles of the right angle with the hypotenuse. Right triangles have special properties that are important to determine trigonometric ratios, such as sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot). ![]()
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