Understanding Vector Calculus & Trigonometry for Physics

AI Thread Summary
The discussion centers on the challenges faced in understanding vector calculus and trigonometry within the context of physics. The original poster expresses frustration with the application of derivatives to vectors and struggles to grasp concepts such as the length of a vector represented by r(t) = r(i*coswt + j*sinwt). There is a specific inquiry about how to interpret the statement that the length of the vector is one and how to apply the length formula |r|=sqrt(a^2 + b^2) to the given equation. Recommendations for clear and intuitive textbooks are sought, with a mention of a previous attempt with "Calculus: An Intuitive and Physical Approach" by Morris, which was found lacking in trigonometry explanations. The discussion also notes that posts focusing solely on mathematical aspects have been redirected to a separate thread.
christian0710
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Hi.

Every time i read physics I feel so discouraged by my lack of understanding in terms of vector calculus and trigonometry. I do understand basic trigonometry and basic vectors but when professors or textbooks move onto combining derivatives with vectors i lack understanding of which rules apply to vectors when combined with calculus, and also how to interprete it. I really need some good book recomendations for brushing up on this and understanding it clearly and intuitively.

And example would be the motion of a particle where r(t) is a vector and i,j are unit vectors.
r(t) = r(i*coswt + j*sinwt)

The professor says "we can see from this that the length of the vector is one" But for me this does not make sense, how can we see this, and how do we apply the length formyla |r|=sqrt(a^2 + b^2) on the r(t) equation?

Please help me with some good physics/calculus math books, that are easy and clear to understand and explain the subjects in detail.

I did try Calculus: An Intuitive and Physical Approach by Morris, but i don't find that it explains trigonometry very well and had to quit after the first 100 pages.
 
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