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Does Trigonometry come before or after Calculus? And


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Does it matter if she takes it before or after Geometry or in conjunction with it? She's loathing Geo. right now and i'm thinking of getting LOF Trigonometry for her to read through and get as much as she can from it.

 

It is completely impossible to understand trigonometry if you have not studied geometry.

Trigonometry is introduced through relationships about right triangles (and later generalized to other situations). If you have not studied triangles, trigonometry makes no sense.

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I thought Trig and Calc are two very different things. Calc is Algebra based and Trig is Geometry based. So does it really matter??

I have been told by several people that if your child is good at Geometry to go with Trig. Good at Algebra then go with Calc.

 

 

Calculus is not "algebra based". A real understanding of calculus requires geometry. The concept of a derivative is developed starting from the slope of a line. The concept of the integral requires the calculation of an area under a curve. Both are geometrical concepts.

Students who can not understand the underlying geometry may be able to memorize formulas for derivatives of certain functions - but that is not understanding calculus.

In addition, the trigonometric functions themselves have, of course, integrals and derivatives who should be investigated in a calculus class.

 

Another aspect is that it is typically the geometry course where students are introduced to the technique of a rigorous mathematical proof, because geometry lends itself very nicely to that. It would be beneficial for an understanding of the proofs involved in calculus if the student is familiar with mathematical proofs - learning to do those at the more abstract calculus material will be rather difficult.

 

OTOH, not being good at algebra will give a student serious trouble in trigonometry. There is quite a bit of algebra involved.

 

I have been told by several people that if your child is good at Geometry to go with Trig. Good at Algebra then go with Calc.

 

 

Are those people who use trigonometry and calculus for their daily lives and have a thorough knowledge of both on college level? If not, I would not consult them for advice regarding mathematics.

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At my little brother's high school, they have the math sequence laid out for trigonometry to come after calculus. Though that's AP trig, and I think they covered some basic trig in his Honors Algebra 3/4 class (second year of algebra). No seperate trigonometry class before calc, though.

 

For clarification, there is no such thing as "AP trig". The only AP math courses are Calc AB (Differential Calculus) or Calc BC (Differential and Integral Calc).

 

The only Calculus courses that are offered without a trigonometric component would be Business Calculus or some sort of Polynomial Calculus for Poets (by this I mean an introduction to Calculus for non-science, non-business students).

 

Most high schools do not offer a separate trig course. Trig is usually introduced in geometry. Some students see more trig in Algebra II. Others are not really exposed until Precalculus.

 

I would be highly suspicious of any mathematics program that offers calculus before trigonometry. It just doesn't make sense.

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