en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

0.86<= cos^{2(10)}((68)/n)

Solution

0.86 \leq cos^{2 (10)} (\frac{68}{n})

Solution

cos (\frac{68}{n}) \geq 0.99248 \dots

Solution steps

0.86 \leq cos^{2 \cdot 10} (\frac{68}{n})

Switch sides

cos^{2 \cdot 10} (\frac{68}{n}) \geq 0.86

Rewrite in standard form

cos^{2 \cdot 10} (\frac{68}{n}) \geq 0.86

Simplify

cos^{20} (\frac{68}{n}) \geq 0.86

Subtract

0.86

from both sides

cos^{20} (\frac{68}{n}) - 0.86 \geq 0.86 - 0.86

Simplify

cos^{20} (\frac{68}{n}) - 0.86 \geq 0

cos^{20} (\frac{68}{n}) - 0.86 \geq 0

Move

0.86

to the right side

cos^{20} (\frac{68}{n}) - 0.86 \geq 0

Add

0.86

to both sides

cos^{20} (\frac{68}{n}) - 0.86 + 0.86 \geq 0 + 0.86

Simplify

cos^{20} (\frac{68}{n}) \geq 0.86

cos^{20} (\frac{68}{n}) \geq 0.86

For

u^{n} \geq a

, if

n

is even then

u \leq - n a or u \geq n a

cos (\frac{68}{n}) \leq - 20 0.86 or cos (\frac{68}{n}) \geq 20 0.86

20 0.86 = 0.99248 \dots

20 0.86

20 0.86 = 0.99248 \dots

= 0.99248 \dots

cos (\frac{68}{n}) \leq - 0.99248 \dots or cos (\frac{68}{n}) \geq 0.99248 \dots

Merge Overlapping Intervals

cos (\frac{68}{n}) \geq 0.99248 \dots

Popular Examples

pi/2 cos((pi*x)/2)>0

\frac{π}{2} cos (\frac{π \cdot x}{2}) > 0

cos(x)>(((1))/((2)))

cos (x) > (\frac{( 1 )}{( 2 )})

- 1 < tan (x) < 1

0<cos(θ)<= sqrt(3)sin(θ)

0 < cos (θ) \leq 3 sin (θ)

sin(t)<0\land cos(t)<0

sin (t) < 0 and cos (t) < 0