How to Learn Trigonometry Washington DC

Steps

1. Brush up your basic mathematical skills. These include knowledge of algebra and algebraical manipulation as well as geometry.
   • Practice algebraic manipulation. Algebraic manipulation is a very basic skill that is necessary to study any branch of mathematics.
     1. Learn to change the subject of any equation.
     2. Learn to solve linear and quadratic equations.
     3. Learn to solve simultaneous linear equations and linear/quadratic pairs of simultaneous equations.
   • Learn basic geometry. Geometry is very closely related to trigonometry and plays a vital part in solving trigonometric problems.
     1. Learn the properties of a circle.
     2. Learn the properties of the interior and exterior angles of polygons including triangles.
     3. Learn the three different types of triangles i.e. isosceles, equilateral, and scalene.
2. Start with studying right-angled triangles. Right angled triangles are easy to study and will give you a good grasp of basic trigonometry and the three trigonometric ratios.
   • Familiarize yourself with the three sides of a right-angled triangle.
     1. The hypotenuse is the side opposite the right angle. It is the biggest side of any right triangle.
     2. The two other sides are called the legs of the triangle. If you pick any angle in the triangle (besides the right angle), you will see that one leg is adjacent to the angle, and the other leg is opposite the angle.
   • Familiarize yourself with the three trigonometric ratios, the base of trigonometry:
     1. The Sine of any angle is the ratio of the length of the side opposite it to the length of the hypotenuse.
     2. The Cosine of any angle is the ratio of the length of the side adjacent to it to the length of the hypotenuse.
     3. The Tangent of any angle is the ratio of the Sine of the angle to the Cosine of the angle. It is often also taken as the ratio of the opposite to the adjacent. The first definition is especially of help in solving trigonometric equations and proving identities while the second is sufficient for a basic study of trigonometry.
3. Move on to non-right triangles.. Because non-right triangles do not have a right angle (that's kind of the definition), the three trigonometric ratios play a smaller role here (although they can also be used in some situations). Rather, two other rules become very important: The Sine Rule, and The Cosine Rule. The following articles explain these rules in detail.How to Use The Sine RuleHow to Use the Cosine Rule
4. Learn to measure angles in radians. Radians are an alternate to degrees as a way of measuring angles. In 180o, there are pi, or approximately 3.142, radians. Radians are especially useful when it comes to investigating the properties of a circle, and are also used in physics in the study of waves and simple harmonic motion.
5. Learn the other three trigonometric ratios. There are three more trigonometric ratios:
   1. Cosecant. Cosecant, Cosec, or csc, is the reciprocal of the sine i.e. 1/sin.
   2. Secant. Secant, or sec, is the reciprocal of the cosine.
   3. Cotangent. Cotangent, or cot, is the reciprocal of the tangent.
6. Practice solving trigonometric equations. Trigonometric equations are (you guessed it) equations involving trigonometric functions. Trigonometric equations can usually be solved by manipulating the equation to contain only one trigonometric ratio. The following methods are used to convert an equation containing more than one trigonometric ration into an equation that contains only one:
   • Dividing the whole equation by a trigonometric term. For example, if an equation has a term in sine as well as a term in cosine, divide the whole equation by cosine. The term in sine becomes a term in tan, and the term in cosine becomes 1. Thus you have an equation only containing tan.
   • Using a trigonometric identity. Trigonometric identities are "equations" that are always true. Two trigonometric identities are written below:sin2x + cos2x = 11 + tan2x = sec2x.Thus if you had an equation containing one term in sine2x and one in cosx, you would replace the term in sine2x with 1 - cos2x from the first identity above. That would result in a quadratic in cosx, which you should know how to solve (says so in the first step).

Tips

• Review algebra and geometry, especially if you are weak.
• If you have problems, ask a teacher or a good student.
• Remember that mathematics is a way of thinking, not a bunch of formulae to learn. Develop your concepts and sharpen your thinking skills through solving problems.

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