14.79m=((7.61_{0}^2sin(2θ_{0}))/g)

Solution

14.79 m = (\frac{7.6 1 _{0}^{2} sin ( 2 θ _{0} )}{g})

θ_{0} = \frac{arcsin ( 0.25538 \dots m g )}{2} + πn, θ_{0} = \frac{π}{2} + \frac{arcsin ( - 0.25538 \dots m g )}{2} + πn

Solution steps

14.79 m = (\frac{7.6 1 _{0}^{2} sin ( 2 θ _{0} )}{g})

Switch sides

\frac{7.6 1 _{0}^{2} sin ( 2 θ _{0} )}{g} = 14.79 m

Multiply both sides by

g

57.9121 sin (2 θ_{0}) = 14.79 m g; g \neq = 0

Divide both sides by

57.9121; g \neq = 0

sin (2 θ_{0}) = 0.25538 \dots m g; g \neq = 0

Apply trig inverse properties

2 θ_{0} = arcsin (0.25538 \dots m g) + 2 πn, 2 θ_{0} = π + arcsin (- 0.25538 \dots m g) + 2 πn

Solve

2 θ_{0} = arcsin (0.25538 \dots m g) + 2 πn : θ_{0} = \frac{arcsin ( 0.25538 \dots m g )}{2} + πn

Solve

2 θ_{0} = π + arcsin (- 0.25538 \dots m g) + 2 πn : θ_{0} = \frac{π}{2} + \frac{arcsin ( - 0.25538 \dots m g )}{2} + πn

θ_{0} = \frac{arcsin ( 0.25538 \dots m g )}{2} + πn, θ_{0} = \frac{π}{2} + \frac{arcsin ( - 0.25538 \dots m g )}{2} + πn

2 cos (x) + 3 cos (x) - 2 = 0

sec (\frac{5 θ}{4}) = 2, [0.2 π]

cos (x) + ∣ cos (x) ∣ = 1, - 2 π \leq x \leq 2 π

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

sec (x + \frac{π}{4}) = - 2, - π \leq x \leq π