Formula of tan theta

how is tan squared less 1 = secant? Each question for this section uses this central calculation to simplify the calculations, but it makes no logical sense We must simplify (tan^2 theta - 1) <<<< note the 1 within this argument, we're taking an angle, and deducting 1 Start by simplifying the tan^2 theta angle tan^2 = sin^2+cos^2 = 1 << this we can agree on the solutions tell us to divide both sides by cos^2. so sin^2/cos^2 + cos^2/cos^2 = 1/cos^2 and 1/cos^2 is sec^2 << still following then somehow it says therefore tan^2-1 = sec^2 so it replaces the entire first argument with sec^2, completely ignoring that 1 we were supposed to deduct from tan. how is this possible? tan^2 is equal to sec^2 according to the calculations, they're just ignoring the one at the end of that original argument we're trying to simplify, like it wasn't there. If sin^2 + cos^2 =tan^2 = 1 then tan^2 - 1 should theoretically be 0, I know this isn't the answer, but you can see that the 1 in tan^2 - 1 can't be ignored, it's not the 1 from the calculation of tan^2, so how can the simplification of tan^2 wipe out this 1? tan²θ = sin²θ + cos²θ = 1 That is wrong. tan²θ = sin²θ/cos²θ. Secondly, the identity is tan²θ + 1 = sec²θ, not tan²θ - 1. Maybe this proof will be easier to follow: tan²θ + 1 = sin²θ/cos²θ + 1 = sin²θ/cos²θ + cos²θ/cos²θ = (sin²θ + cos²θ)/cos²θ //sin²θ + cos²θ = 1, which we substitute in. = 1/cos²θ = sec²θ Therefore, tan²θ + 1 = sec²θ. The process is somewhat confusing to find the exact...

Table of Contents • • • • • • • • WHAT IS SOHCAHTOA? Sine, cosine, and tangent are the three fundamental trigonometric functions in The table below shows the meaning behind the mnemonic SOHCAHTOA and its corresponding formula. Meaning Formula SOH SOH means $\sin \theta$is equal to the opposite divided by the hypotenuse. $\sin \theta =\frac$ There are other ways to remember the three fundamental trigonometric functions aside from the mnemonic SOHCAHTOA. The list below shows some of the other mnemonics one can use to familiarize yourselves with Mnemonics for Sine, Cosine, and Tangent Some Of Her Children Are Having Trouble Over Algebra She Offered Her Cat A Heaping Teaspoon Of Acid Saddle Our Horses, Canter Away Happily, To Other Adventures. School! Oh, How Can Anyone Have Trouble Over Academics? Some Old Horse Caught Another Horse Taking Oats Away. Two Old Angels Skipped Over Heaven Carrying Ancient Harps The Ordinary Army Simple Officers Have Curly Auburn Hair WHEN ARE THE PARTS OF A RIGHT TRIANGLE? SOHCAHTOA can help us determine unknown measure The hypotenuse is the longest side of a right triangle. It is the side opposite to the right angle. The opposite side is the side opposite to the given angle. The adjacent side is the non-hypotenuse side that is next to the given angle. Always remember that the adjacent side is always next to the given angle. Say, for example, we have ∆ABCas shown in the figure below: SOLUTION Given that the right angle is ∠D, we can easily say th...

We have the following general formulas: • \(\) Display The Proof Let's invoke \[\cos(n\theta) + i\sin(n\theta) = \big(\cos(\theta) + i\sin(\theta) \big)^n.\] Since \(n\) is a positive integer, the Hence, by expanding, we have \[\big(\cos(\theta) + i\sin(\theta) \big)^n= \cos^n(\theta) + n\cos^.\] Hence, our proof is complete. \(_\square\) For angles \(\theta_1, \theta_2, \theta_3, \ldots\), we have • \(.\) We'll show here, without using any form of Taylor's series, the expansion of \(\sin(\theta), \cos(\theta), \tan(\theta)\) in terms of \(\theta\) for small \(\theta\). Here are the generalized formulaes: • \(.\) We have the following general formulas: If \(n\) is even, • \(.\) Display the Proof Sorry. This section is temporarily empty. It will be completed as soon as possible. If \(n\) is odd, • \(.\)

how is tan squared less 1 = secant? Each question for this section uses this central calculation to simplify the calculations, but it makes no logical sense We must simplify (tan^2 theta - 1) <<<< note the 1 within this argument, we're taking an angle, and deducting 1 Start by simplifying the tan^2 theta angle tan^2 = sin^2+cos^2 = 1 << this we can agree on the solutions tell us to divide both sides by cos^2. so sin^2/cos^2 + cos^2/cos^2 = 1/cos^2 and 1/cos^2 is sec^2 << still following then somehow it says therefore tan^2-1 = sec^2 so it replaces the entire first argument with sec^2, completely ignoring that 1 we were supposed to deduct from tan. how is this possible? tan^2 is equal to sec^2 according to the calculations, they're just ignoring the one at the end of that original argument we're trying to simplify, like it wasn't there. If sin^2 + cos^2 =tan^2 = 1 then tan^2 - 1 should theoretically be 0, I know this isn't the answer, but you can see that the 1 in tan^2 - 1 can't be ignored, it's not the 1 from the calculation of tan^2, so how can the simplification of tan^2 wipe out this 1? tan²θ = sin²θ + cos²θ = 1 That is wrong. tan²θ = sin²θ/cos²θ. Secondly, the identity is tan²θ + 1 = sec²θ, not tan²θ - 1. Maybe this proof will be easier to follow: tan²θ + 1 = sin²θ/cos²θ + 1 = sin²θ/cos²θ + cos²θ/cos²θ = (sin²θ + cos²θ)/cos²θ //sin²θ + cos²θ = 1, which we substitute in. = 1/cos²θ = sec²θ Therefore, tan²θ + 1 = sec²θ. The process is somewhat confusing to find the exact...

Table of Contents • • • • • • • • WHAT IS SOHCAHTOA? Sine, cosine, and tangent are the three fundamental trigonometric functions in The table below shows the meaning behind the mnemonic SOHCAHTOA and its corresponding formula. Meaning Formula SOH SOH means $\sin \theta$is equal to the opposite divided by the hypotenuse. $\sin \theta =\frac$ There are other ways to remember the three fundamental trigonometric functions aside from the mnemonic SOHCAHTOA. The list below shows some of the other mnemonics one can use to familiarize yourselves with Mnemonics for Sine, Cosine, and Tangent Some Of Her Children Are Having Trouble Over Algebra She Offered Her Cat A Heaping Teaspoon Of Acid Saddle Our Horses, Canter Away Happily, To Other Adventures. School! Oh, How Can Anyone Have Trouble Over Academics? Some Old Horse Caught Another Horse Taking Oats Away. Two Old Angels Skipped Over Heaven Carrying Ancient Harps The Ordinary Army Simple Officers Have Curly Auburn Hair WHEN ARE THE PARTS OF A RIGHT TRIANGLE? SOHCAHTOA can help us determine unknown measure The hypotenuse is the longest side of a right triangle. It is the side opposite to the right angle. The opposite side is the side opposite to the given angle. The adjacent side is the non-hypotenuse side that is next to the given angle. Always remember that the adjacent side is always next to the given angle. Say, for example, we have ∆ABCas shown in the figure below: SOLUTION Given that the right angle is ∠D, we can easily say th...

We have the following general formulas: • \(\) Display The Proof Let's invoke \[\cos(n\theta) + i\sin(n\theta) = \big(\cos(\theta) + i\sin(\theta) \big)^n.\] Since \(n\) is a positive integer, the Hence, by expanding, we have \[\big(\cos(\theta) + i\sin(\theta) \big)^n= \cos^n(\theta) + n\cos^.\] Hence, our proof is complete. \(_\square\) For angles \(\theta_1, \theta_2, \theta_3, \ldots\), we have • \(.\) We'll show here, without using any form of Taylor's series, the expansion of \(\sin(\theta), \cos(\theta), \tan(\theta)\) in terms of \(\theta\) for small \(\theta\). Here are the generalized formulaes: • \(.\) We have the following general formulas: If \(n\) is even, • \(.\) Display the Proof Sorry. This section is temporarily empty. It will be completed as soon as possible. If \(n\) is odd, • \(.\)