ok so I'm learning to solve problems like
cos(x)=2
and
sin(x)=5
I've wrapped my head around the process required to do so and I must say my brain is like @_@ mosh right now. Whenever I ask this question I never get a direct answer. I understand it's important to be able to define such angles and that this field of math is a valid field and worth studying but why??? Why would I ever need to know how to do this? Like it really hurts my head and I don't see when I would ever need to be able to solve such a problem in real life other than a text book...
55-65
I agree with you... I will not be able to solve for x either, when I am given
cos(x)=2, or sin(x)=5.
The reason is because for any real value of x, cos(x) and sin(x) vary between -1 and +1. This means that the solutions to the two given equations do not exist!
I hope you have not made a typo, unless your teacher is training you to think outside of the box.
As to whether you'll ever going to need to know how to solve these problems, it all depends on what you want to do later in life. If you want to flip burgers for the rest of your life, you will never need to know this stuff. If you will be doing renovations, landscaping, and a whole lot of "ordinary guy" jobs, this skill will definitely help you.
By the way George, you said you have done the programming exercises for the whole computer programming textbook before classes even started, you could not possibly have this cos(x) problem bother you, could you?
May I also add computer programming as one of the areas where trigonometry would be a definite asset?
I understand that solving trigonometric equations like cos(x) = 2 or sin(x) = 5 can be challenging and may seem abstract at first. However, trigonometry has many practical applications in various fields, including physics, engineering, architecture, computer graphics, and navigation.
Let's take a closer look at some examples where solving trigonometric equations is useful:
1. Physics: Trigonometry is essential for understanding and predicting the motion of objects. For instance, when studying projectile motion, you may need to find the angle at which an object should be launched to reach a certain distance or height.
2. Engineering: Trigonometry is used extensively in engineering disciplines. Engineers often work with angles and distances, and trigonometric principles are applied in areas such as structural analysis, electrical circuits, signal processing, and control systems.
3. Architecture: Architects rely on trigonometry for designing buildings, bridges, and other structures. Trigonometric calculations are used to determine angles, slopes, and dimensions, ensuring that buildings stand strong and are aesthetically pleasing.
4. Computer Graphics: Trigonometry plays a crucial role in creating computer-generated images, animations, and video games. By manipulating angles and distances, trigonometric functions enable the rendering of realistic three-dimensional objects and animations.
5. Navigation: Trigonometry is used in navigation tools like compasses, GPS systems, and celestial navigation. By understanding trigonometric relationships, sailors, pilots, and hikers can determine their position, direction, and distance traveled.
These are just a few examples of how trigonometry is practical and applicable in real-life scenarios. While it may seem challenging and abstract at first, mastering trigonometric equations can provide a solid foundation for problem-solving in various fields.