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What Is It
Trigonometry is a topic dedicated to trigonometric functions sine, cosine, tangent, their reciprocals cosecant, secant, and cotangent, and each of their inverse functions denoted by adding “arc” before the name of the function. The basis of these functions is the relationships of angles and side lengths of triangles. Trigonometry usually focuses on right triangles, triangles with one 90 degree angle.
Assume a right triangle with angle theta (?); theta is not the 90 degree angle. Theta will always have the hypotenuse (longest part of the triangle, diagonal side) on one side and an adjacent leg on the other. The remaining leg will be on the opposite side of the triangle. The main three relationships are as follows:
sin??=(length of opposite leg)/(length of hypotenuse)
cos??=(length of adjacent leg)/(length of hypotenuse)
tan???=(length of opposite leg)/(length of adjacent leg)=sin??/cos?? ?
These three relationships form the basis for all other trigonometric functions and identities. To find cosecant, secant, and cotangent, divide one by sin, cos, and tan respectively. This can also be expressed in the form of csc(?) = sin(?)-1. To find the inverse functions, the function itself is to be put to the power of -1. Note that asin(?) = sin -1 (?) ? sin(?)-1. Identities are equations which are true for right triangles. In addition to the equations above, there is the Pythagorean Theorem, opposite angle identities, double angle identities, half angle identities, product-sum identities, product identities, triple angle formulas, and Ptolemy’s identities. Ptolemy’s identities are also known as sum and difference formulas for sine and cosine. The Pythagorean Theorem states the following, where a and b are legs of a triangle and c is the hypotenuse
a^2+b^2=c^2 or sin^2?(?)+cos^2??(?)?=1
While the other listed are important, they do not need to be memorized unless an instructor requires doing so for their class. Having a readily accessible reference sheet should suffice for homework and practical applications. As students progress through trigonometry, they will learn how to derive and utilize these identities. Students will often be asked to use known identities to convert a value into an equivalent expression. As a prerequisite to calculus and differential equations, almost every traditional college or high school student will take trigonometry. Furthermore, students can expect to see basic trigonometry on exams like the SAT, ACT, and ASVAB.
How Prep Helps
Taking trigonometry preparatory courses gives students the chance to hit the ground running when they take trigonometry at their high school or college. At Miles Smart Tutoring, we are equipped with highly trained and educated individuals that can reinforce vital topics, provide guidance while completing practice problems, and teach problem-solving techniques to help students optimize time during exams. These techniques will not only help with your current math class, but future math and science courses and standardized tests such as the SAT/ACT.
Customization of Tutoring Courses
At Miles Smart Tutoring, we have instructors who are experienced in assessing and tailoring their lessons to meet the specific needs of each individual student and learning style. We take the time to connect the tutor that would best meet the needs of the student, ensuring a good partnership.
Our trigonometry tutors have knowledge that extends past doing well in BC Calculus and can also provide insight to career paths that require mathematics. For example, one tutor has a degree in mechanical engineering from the University of Florida and was a teaching assistant for a mid-level engineering course. Another tutor is a student and teaching assistant in electrical engineering at Florida Polytechnic University.
The high caliber of our tutors means each student will obtain instruction without hesitation and with as much detail as the student’s needs demand. Our tutor’s dedicated experience, training, and education is what allows our instructors to teach in a way that will allow students to get the most out of their time together. Each student learns differently, so our tutors aspire to help each individual student by assessing their unique pathways for learning and modifying their instructing to create methods for their students to absorb the material that works best for them.