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Popular >

(-1)/(16)sec^3(t)>0

Solution

\frac{- 1}{16} sec^{3} (t) > 0

Solution

False for all t \in R

Solution steps

\frac{- 1}{16} sec^{3} (t) > 0

Express with sin, cos

\frac{- 1}{16} sec^{3} (t) > 0

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

\frac{- 1}{16} (\frac{1}{cos ( t )})^{3} > 0

\frac{- 1}{16} (\frac{1}{cos ( t )})^{3} > 0

Divide both sides by

- 0.0625

\frac{\frac{- 1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625} > \frac{0}{- 0.0625}

Refine

\frac{\frac{- 1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625} > \frac{0}{- 0.0625} : \frac{1}{cos ^{3} ( t )} > 0

\frac{\frac{- 1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625} > \frac{0}{- 0.0625}

Simplify

\frac{\frac{- 1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625} : \frac{1}{cos ^{3} ( t )}

\frac{\frac{- 1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= \frac{- \frac{1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{- 0.0625}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{\frac{1}{16} ( \frac{1}{c o s ( t )} ) ^{3}}{0.0625}

(\frac{1}{cos ( t )})^{3} = \frac{1}{cos ^{3} ( t )}

(\frac{1}{cos ( t )})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{3}}{cos ^{3} ( t )}

Apply rule

1^{a} = 1

1^{3} = 1

= \frac{1}{cos ^{3} ( t )}

= \frac{\frac{1}{16} \cdot \frac{1}{c o s ^{3} ( t )}}{0.0625}

Multiply

\frac{1}{16} \cdot \frac{1}{cos ^{3} ( t )} : \frac{1}{16 cos ^{3} ( t )}

\frac{1}{16} \cdot \frac{1}{cos ^{3} ( t )}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{16 cos ^{3} ( t )}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{16 cos ^{3} ( t )}

= \frac{\frac{1}{16 c o s ^{3} ( t )}}{0.0625}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1}{16 cos ^{3} ( t ) \cdot 0.0625}

Multiply:

16 cos^{3} (t) \cdot 0.0625 = cos^{3} (t)

= \frac{1}{cos ^{3} ( t )}

\frac{0}{- 0.0625} = 0

\frac{0}{- 0.0625}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\frac{1}{cos ^{3} ( t )} > 0

\frac{1}{cos ^{3} ( t )} > 0

If

\frac{1}{a} > 0

then

a > 0

cos^{3} (t) > 0

No Solution for t \in R

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