Online Trigonometry Tutors

Online Trigonometry Tutors Trigonometry is one of the important and commonly used sections of Mathematics. Trigonometry is the study of measure of the angles and sides in triangles and other geometric structures. In trigonometry, right triangles are often used to calculate the measurements. But when required, the trigonometric functions are also extended to calculate the measurements of other types of triangles given the appropriate information. The trigonometric identities and formulas make the calculations much simpler and easy to analyze the measure of the angles and the sides in a triangle. Example 1: In right triangle ABC, side AC is the hypotenuse. If given the measure of angle C as 45 and the length of side AC is 4m, then what is the length of side AB? Based on the question, here is the diagram. The trigonometric function, sin(C) = (opposite side)/ (hypotenuse) Therefore, sin(C) = AB/AC This gives: sin(45)= AB/ 4 - 1/2= AB/ 4 This implies: AB= 4 * 1/2 - 4 * 2/ 2 = 22 Therefore the measure of the side, AB= 22m Example 2: Prove the given trigonometric identity: tan(x)/ cot(x) = [(sin(x)/cos(x)]2 Here lets start with the left-hand side of the equation - tan(x)/ cot(x) We can also write the above expression as: tan(x)/ cot(x) = [sin(x/cos(x)]/ [cos(x)/sin(x)] Here we can take the reciprocal of the denominator and this gives: [sin(x)/ cos(x)] * [sin(x)/cos(x)] This implies: [sin(x)]2/ [cos(x)]2 which can also be written as: [sin(x)/ cos(x)]2 = right-hand side of the equation! Hence proved! Online Trigonometry Tutors Trigonometry is a branch of Mathematics and it is the study of the measure of the angles and the sides in a triangle using the trigonometric functions. In Trigonometry, there are 6 important functions and they are sine, cosine, tangent, cosecant, secant and cotangent of a given particular angle. Each trigonometric function has its own specific graph and there are also trigonometric identities and formulas which relate these functions together. Also based on different angles like half-angles, double-angles etc. we have the trigonometric formulas relating the functions together. Example 1: If is an angle in the first quadrant and sin() = 3/5 and cos() = 4/5, then what is the value of sin(2)? Given sin() = 3/5 and cos() = 4/5 In order to find the value of sin(2), we can use the double-angle formula. According to the trigonometric double-angle formula: sin(2) = 2 * sin() * cos() Hence substituting the given values in the above formula we get: sin(2) = 2 * 3/5 * 4/5 This gives: sin(2) = 24/25 Therefore the value of sin(2) = 24/25. Example 2: If is an angle in the first quadrant and sin() = 3/5 and cos() = 4/5, then what is the value of cos(2)? Given sin() = 3/5 and cos() = 4/5 In order to find the value of cos(2), we can use the double-angle formula. According to the trigonometric double-angle formula: cos(2) = cos2() sin2() Hence substituting the given values in the above formula we get: cos(2) = (4/5)2 (3/5)2 = 16/25 9/25 This gives: cos(2) = 7/25 Therefore the value of cos(2) = 7/25.