One way to remember the letters is to sound them out phonetically (i.e. Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English: SOH-CAH-TOA Image mnemonic to help remember the ratios of sides of a right triangle However, it is important to note that this trick only covers a portion of the unit circle, and additional techniques may be needed to remember the values of the angles in the other three quadrants.In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions.
Using this hand trick can help you quickly remember the trigonometric values of the angles in the first quadrant of the unit circle. This line represents the angle of 90 degrees on the unit circle, where the sine value is 1 and the cosine value is 0. This “U” represents the angle of 60 degrees on the unit circle, where the sine value is √3/2 and the cosine value is 1/2.įinally, move your index finger to touch the tip of your pinky finger, creating a straight line. Move your index finger to touch the base of your pinky finger, creating a “U” shape. This line represents the angle of 45 degrees on the unit circle, where both the sine and cosine values are equal to √2/2. Move your index finger again to touch the tip of your thumb, creating a straight line.
This “L” represents the angle of 30 degrees on the unit circle, where the sine value is 1/2 and the cosine value is √3/2. Now, move your index finger to touch the middle of your thumb, creating an “L” shape. This “O” represents the angle of 0 degrees on the unit circle, where both the sine and cosine values are equal to 1. Touch the tip of your index finger to the base of your thumb, creating a small “O” shape. Make a fist with your thumb tucked inside. Start by holding your left hand up with your palm facing away from you. This trick is sometimes called “SOHCAHTOA on the hand” or “Handy Acronym.” Here’s how it works: There is a hand trick that can be used to remember the trigonometric values of the angles in the first quadrant of the unit circle. These can be a helpful supplement to your studying and practice. Use technology: There are many online resources and apps that can help you practice using the unit circle and test your knowledge.
Drawing the unit circle and labeling the angles and values can also be helpful.
Visualize the circle: Try to visualize the unit circle in your mind, and imagine each angle and its corresponding values. For example, “All Students Take Calculus” can be used to remember the signs of each function in each quadrant: All (positive in quadrant I), Students (sine is positive in quadrant II), Take (tangent is positive in quadrant III), Calculus (cosine is positive in quadrant IV). Use mnemonics: Mnemonics can be a helpful way to remember the values of the trigonometric functions at different angles. Try working through problems and exercises that involve using the unit circle, and make sure to review regularly. Practice, practice, practice: The more you practice using the unit circle, the easier it will be to remember. For example, the angles 0°, 90°, 180°, and 270° are often referred to as the “cardinal angles” and their values are easy to memorize (cos 0° = 1, sin 0° = 0, cos 90° = 0, sin 90° = 1, and so on). Use patterns: Many of the angles and their corresponding trigonometric values follow patterns. Memorizing the unit circle can be a daunting task, but there are some techniques that can help make it easier:
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