What is the general solution for 10sin(x)+4=10 ?

The general solution for 10sin(x)+4=10 is x=0.64350…+2pin,x=pi-0.64350…+2pin

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10sin(x)+4=10

10 sin (x) + 4 = 10

x = 0.64350 \dots + 2 πn, x = π - 0.64350 \dots + 2 πn

Degrees

x = 36.86989 \dots^{\circ} + 36 0^{\circ} n, x = 143.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

10 sin (x) + 4 = 10

Move

4

to the right side

10 sin (x) + 4 = 10

Subtract

4

from both sides

10 sin (x) + 4 - 4 = 10 - 4

Simplify

10 sin (x) = 6

10 sin (x) = 6

Divide both sides by

10

10 sin (x) = 6

Divide both sides by

10

\frac{10 sin ( x )}{10} = \frac{6}{10}

Simplify

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Apply trig inverse properties

sin (x) = \frac{3}{5}

General solutions for

sin (x) = \frac{3}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

x = arcsin (\frac{3}{5}) + 2 πn, x = π - arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

x = 0.64350 \dots + 2 πn, x = π - 0.64350 \dots + 2 πn

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

cos^{2} (x) - 4 cos (x) + 4 = 0

t, x - 4 = sec^{2} (t)

csc (θ) = \frac{34}{3}, cos (θ) > 0

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) = 0

What is the general solution for 10sin(x)+4=10 ?
The general solution for 10sin(x)+4=10 is x=0.64350…+2pin,x=pi-0.64350…+2pin