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Trigonometry and Calculus: Proof
Students sometimes use a formula without thinking about its origin
or why it makes sense. Students also often believe a particular
statement or definition is true if they can find one or two examples
of the statement. Each of the problems below requires students to
prove either a formula or a statement.
To help in understanding the concept of proof and learning about
writing proofs in general, you can visit the Dr. Math FAQ on
Proof. For additional background
information elsewhere on our site, explore the
High School Trigonometry
and Calculus
areas of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Trigonometry and
Calculus (Single Variable)
in our Internet Mathematics Library.
Access to these problems requires a Membership.
-
Can You Prove It?
- Leigh Nataro
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Trig/Calc, difficulty level 3. Prove that the square root of 2 is irrational, and explain how to use a straightedge and compass to construct a segment that is the square root of 2 in length.
... more>>
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Ellipse Areas
- Leigh Nataro
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Trig/Calc, difficulty level 3. Use calculus to show that the area of an ellipse is pi*a*b.
... more>>
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Is It a Midpoint?
- Leigh Nataro, Andrea Medini
-
Trig/Calc, difficulty level 3. Prove that the point of inflection of a cubic function is the midpoint of the segment that connects the function minimum and the function maximum.
... more>>
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A Parabola Proof
- Leigh Nataro
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Trig/Calc, difficulty level 3. Prove that the area of a parabola is 2/3 the product of its width and height.
... more>>
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Pete's Predictions
- Leigh Nataro
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Trig/Calc, difficulty level 2. Verify the formula for finding the maximum height of a ball thrown upward.
... more>>
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Rationals and Irrationals
- Asher Walkover
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Trig/Calc, difficulty level 2. Can you sum two irrationals and get a rational? Can you take an irrational number to an irrational power and get a rational?
... more>>
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Rolle's Theorem Rediscovered
- John Feminella
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Trig/Calc, difficulty level 3. Prove the Mean Value theorem.
... more>>
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Tangents and Slopes
- Leigh Nataro
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Trig/Calc, difficulty level 3. Use the tangent ratio to show that the product of the slopes of two perpendicular lines is -1.
... more>>
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Triangles, Sines, and Areas
- Leigh Nataro
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Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A).
... more>>
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