Mar 18, 2015 · To calculate $\sec^2{x}$ on a graphing calculator, you should have the ability to write strings of functions with parenthesis and the like and can write it as:

Prove the following trigonometric identity: $$1 + \\tan^2\\theta = \\sec^2\\theta$$ I'm curious to know of the different ways of proving this depending on different characterizations of tangent and se...

Yes, this can be done, but the method is far longer than if you know the derivative of $\tan x$ already. The point is to convert this trigonometric integral into the integral of a rational function, integrate that with partial fractions, and then convert back.

Jun 7, 2020 · If you know the identity $\sec^2x=1+\tan^2x$, then this easily simplifies to: $$\sec^2 x-\tan^2 x$$ $$=(1+\tan^2x)-\tan^2x$$ $$=1$$ But in your question you mentioned reciprocals, so I am assuming you can't use the above identity.

Jul 24, 2019 · I understand why the derivative of $\\sin x$ is $\\cos x$, and why the derivative of $\\cos x$ is $-\\sin x$ in a geometric way. But I can not understand why the derivative of $\\tan x$ is $\\sec^2 x$....

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Apr 21, 2023 · The expression sec²x - tan²x is not a constant function, as it depends on the value of x. However, it can be simplified using trigonometric identities to yield a constant function.

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Jun 14, 2021 · It seems that what we are asked to notice is that $$ \sec^2 x \ + \ \csc^2 x \ \ = \ \ \frac{1}{\cos^2 x} \ + \ \frac{1}{\sin^2 x} \ \ = \ \ \frac{\sin^2 x \ + \ \cos ...

A truck travels along a straight, level road at the speed of 99ft/sec. when the driver is forced to apply the breaks to avoid an accident. If the truck undergoes a constant deceleration of 5ft/sec2, how far does the truck travel before coming to a complete stop?