Select the expression with the same value as the given expression.sec(−4π5)\sec\left(-\frac{4\pi}{5}\right)sec(−54π)

sec ⁡ ( 4 π 5 ) \sec\left(\frac{4\pi}{5}\right) sec ( 5 4 π )

Select the expression with the same value as the given expression. sec ( − 4 π 5 ) \sec\left(-\frac{4\pi}{5}\right) sec ( − 5 4 π )

Here we're asked to select the expression with the same value as the given expression and our given expression here is the secant of negative 4 pi over 5. Now the secant, like cosine, is an even function. So based on that identity here, I know that the secant of negative 4pi over 5 is really just equal to the secant of positive 4 pi over 5 because this function is even. So I see that that's one of my choices here. So I know that this one has the same value as my given pi over 5 as your correct answer. But if this had said 1 over the cosine of 4 pi over 5, that would also be correct, but it doesn't. Now our negative answers are clearly not correct because secant is an even function. So we are only left with our final answer as the secant of 4pi over 5 as our correct choice. Thanks for watching, and I'll see you in the next one.

Select the expression with the same value as the given expression. sec ⁡ ( − 4 π 5 ) \sec\left(-\frac{4\pi}{5}\right) sec ( − 5 4 π )

sec ⁡ ( 4 π 5 ) \sec\left(\frac{4\pi}{5}\right) sec ( 5 4 π )

cos ⁡ ( 4 π 5 ) \cos\left(\frac{4\pi}{5}\right) cos ( 5 4 π )

− cos ⁡ ( 4 π 5 ) -\cos\left(\frac{4\pi}{5}\right) − cos ( 5 4 π )

− sec ⁡ ( 4 π 5 ) -\sec\left(\frac{4\pi}{5}\right) − sec ( 5 4 π )

12. Trigonometric Identities

Introduction to Trigonometric Identities

Precalculus

12. Trigonometric Identities

Introduction to Trigonometric Identities

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Multiple Choice

Select the expression with the same value as the given expression.
$\sec\left(-\frac{4\pi}{5}\right)$

$\cos\left(\frac{4\pi}{5}\right)$

$-\cos\left(\frac{4\pi}{5}\right)$

$\sec\left(\frac{4\pi}{5}\right)$

$-\sec\left(\frac{4\pi}{5}\right)$

Verified step by step guidance

Understand that the secant function, sec(θ), is the reciprocal of the cosine function, cos(θ). Therefore, sec(θ) = 1/cos(θ).

Recognize that the secant function is an even function, meaning sec(-θ) = sec(θ). This property will help simplify sec(-4π/5).

Apply the even function property: sec(-4π/5) = sec(4π/5). This means the expression sec(-4π/5) is equivalent to sec(4π/5).

Now, compare the given options to find the expression that matches sec(4π/5). The correct choice should reflect this equivalence.

Identify that the correct answer is sec(4π/5), as it directly matches the simplified form of the original expression sec(-4π/5).

6:19m

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