Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.
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 45º 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 = 2√2
Therefore the measure of the side, AB= 2√2m
Example 2: Prove the given trigonometric identity: tan(x)/ cot(x) = [(sin(x)/cos(x)]2
Here let’s 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!
HAVE A QUESTION?
Chat With Our Tutoring Experts Now
I just want you to know how great Brinda has been in tutoring me on probability. She is patient and very knowledgeable in all concepts. I look forward to many more sessions with her. I appreciate her help and the great work that Tutor Pace is doing.
9th Grade, from Barbara
Thank you for your excellent tutoring services. It has surely made a lot of difference in our child's academic performance.
9th Grader, from Venkat (father of Sai)
I have enjoyed my session with Aparna and it was helpful. I will hope to see her as my Math tutor in future sessions as well.
10th Grade, from Senia Revayo
Your tutor has been such an inspiration to me as I have difficulty getting some of the physics concepts down and truly understanding them. She takes the time to fully explain each and every aspect of any problem I might ask for help and always with encouragement and humor.