y = x − 2 cos ⁡ x y=x-2\cos x y = x − 2 cos x Has a horizontal tangent on 0 ≤ x < 2 π 0\le x<2\pi 0 ≤ x < 2 π at

x = 7 π 6 x=\frac{7\pi}{6} x = 6 7 π and x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

x = π 6 x=\frac{\pi}{6} x = 6 π and 5 π 6 \frac{5\pi}{6} 6 5 π

x = π 3 x=\frac{\pi}{3} x = 3 π and x = 2 π 3 x=\frac{2\pi}{3} x = 3 2 π

x = 4 π 3 x=\frac{4\pi}{3} x = 3 4 π and x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

x = π 6 x=\frac{\pi}{6} x = 6 π and x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

What is the equation of the tangent line to y = cos x at x = π 3 \frac{\pi}{3} 3 π

y − 1 2 = − 3 2 ( x − π 3 ) y\ -\frac{1}{2}=-\frac{\sqrt{3}}{2}\left(x\ -\ \frac{\pi}{3}\right) y − 2 1 = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ( x − 3 π )

y − π 3 = 1 2 ( x − 1 2 ) y\ -\ \frac{\pi}{3}=\frac{1}{2}\left(x-\frac{1}{2}\right) y − 3 π = 2 1 ( x − 2 1 )

y − 3 2 = 1 2 ( x − π 3 ) y\ -\frac{\sqrt{3}}{2}=\frac{1}{2}\left(x\ -\ \frac{\pi}{3}\right) y − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> = 2 1 ( x − 3 π )

y − 1 2 = 1 2 ( x − π 3 ) y\ -\ \frac{1}{2}=\frac{1}{2}\left(x-\frac{\pi}{3}\right) y − 2 1 = 2 1 ( x − 3 π )

Trig Derivatives Practice

Authored by Angela Walters

Mathematics

9th - 12th Grade

CCSS covered

Used 45+ times

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13 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the derivative of cot(x)?

sec²(x)

-sec²(x)

csc²(x)

-csc²(x)

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the derivative of sin(x)?

-sin(x)

-cos(x)

cos(x)

sin(x)

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

What is the derivative of cos(x)?

sin(x)

-sin(x)

cos(x)

-cos(x)

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the derivative of csc(x)?

csc(x)cot(x)

-csc(x)cot(x)

-csc²(x)

-cot²(x)

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

When we "take the derivative" of a function what are we finding?

What's a derivative?

The rate at which our struggles in Calculus are increasing.

The slope of the secant line

The slope of the tangent line

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

What is the derivative of tan(x)?

-sec²(x)

-csc²(x)

sec²(x)

csc²(x)

What is the derivative of sec(x)?

sec(x)tan(x)

csc(x)cot(x)

-sec(x)tan(x)

-csc(x)cot(x)

10.

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

Which problem below would require the "product rule" ?

$\sin\left(\cos x\right)$

xsinx

$\sin^3x$

$\sin x^{3\ }$

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Trig Derivatives Practice

What is the derivative of cot(x)?

What is the derivative of sin(x)?

What is the derivative of cos(x)?

What is the derivative of csc(x)?

When we "take the derivative" of a function what are we finding?

What is the derivative of tan(x)?

What is the derivative of sec(x)?

Find the derivative.

Find the derivative f(x) = tanxcosx

Which problem below would require the "product rule" ?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

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