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Popular >

sec(-5)sin(θ)>0

Solution

sec (- 5) sin (θ) > 0

Solution

2 πn < θ < π + 2 πn

+2

Interval Notation

(2 πn, π + 2 πn)

Decimal Notation

2 πn < θ < 3.14159 \dots + 2 πn

Solution steps

sec (- 5) sin (θ) > 0

Simplify

sec (- 5) : sec (5)

sec (- 5)

Use the following property:

sec (- x) = sec (x)

sec (- 5) = sec (5)

= sec (5)

sec (5) sin (θ) > 0

Divide both sides by

sec (5)

sec (5) sin (θ) > 0

Divide both sides by

sec (5)

\frac{sec ( 5 ) sin ( θ )}{sec ( 5 )} > \frac{0}{sec ( 5 )}

Simplify

sin (θ) > 0

sin (θ) > 0

For

sin (x) > a

, if

- 1 \leq a < 1

then

arcsin (a) + 2 πn < x < π - arcsin (a) + 2 πn

arcsin (0) + 2 πn < θ < π - arcsin (0) + 2 πn

Simplify

arcsin (0) : 0

arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0

Simplify

π - arcsin (0) : π

π - arcsin (0)

Use the following trivial identity:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= π - 0

π - 0 = π

= π

0 + 2 πn < θ < π + 2 πn

Simplify

2 πn < θ < π + 2 πn

Popular Examples

2sin(x)+sqrt(3)>0

2 sin (x) + 3 > 0

cos^{2} (x) \geq 1

csc(θ)((sqrt(26))/5)tan(θ)<0

csc (θ) (\frac{26}{5}) tan (θ) < 0

(2sin(x)+2)/(cos(x))<= 0

\frac{2 sin ( x ) + 2}{cos ( x )} \leq 0

sin (x) 0 < 2 π