What is the general solution for 30^2=20^2+18^2-2(20)(18)cos(A) ?

The general solution for 30^2=20^2+18^2-2(20)(18)cos(A) is A=1.81774…+2pin,A=-1.81774…+2pin

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30^2=20^2+18^2-2(20)(18)cos(A)

3 0^{2} = 2 0^{2} + 1 8^{2} - 2 (20) (18) cos (A)

A = 1.81774 \dots + 2 πn, A = - 1.81774 \dots + 2 πn

Degrees

A = 104.14900 \dots^{\circ} + 36 0^{\circ} n, A = - 104.14900 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 0^{2} = 2 0^{2} + 1 8^{2} - 2 (20) (18) cos (A)

Switch sides

2 0^{2} + 1 8^{2} - 2 \cdot 20 \cdot 18 cos (A) = 3 0^{2}

Multiply the numbers:

2 \cdot 20 \cdot 18 = 720

2 0^{2} + 1 8^{2} - 720 cos (A) = 3 0^{2}

2 0^{2} = 400

400 + 1 8^{2} - 720 cos (A) = 3 0^{2}

1 8^{2} = 324

400 + 324 - 720 cos (A) = 3 0^{2}

Add the numbers:

400 + 324 = 724

- 720 cos (A) + 724 = 3 0^{2}

3 0^{2} = 900

- 720 cos (A) + 724 = 900

Move

724

to the right side

- 720 cos (A) + 724 = 900

Subtract

724

from both sides

- 720 cos (A) + 724 - 724 = 900 - 724

Simplify

- 720 cos (A) = 176

- 720 cos (A) = 176

Divide both sides by

- 720

- 720 cos (A) = 176

Divide both sides by

- 720

\frac{- 720 cos ( A )}{- 720} = \frac{176}{- 720}

Simplify

\frac{- 720 cos ( A )}{- 720} = \frac{176}{- 720}

Simplify

\frac{- 720 cos ( A )}{- 720} : cos (A)

\frac{- 720 cos ( A )}{- 720}

Apply the fraction rule:

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

= \frac{720 cos ( A )}{720}

Divide the numbers:

\frac{720}{720} = 1

= cos (A)

Simplify

\frac{176}{- 720} : - \frac{11}{45}

\frac{176}{- 720}

Apply the fraction rule:

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

= - \frac{176}{720}

Cancel the common factor:

16

= - \frac{11}{45}

cos (A) = - \frac{11}{45}

cos (A) = - \frac{11}{45}

cos (A) = - \frac{11}{45}

Apply trig inverse properties

cos (A) = - \frac{11}{45}

General solutions for

cos (A) = - \frac{11}{45}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

A = arccos (- \frac{11}{45}) + 2 πn, A = - arccos (- \frac{11}{45}) + 2 πn

A = arccos (- \frac{11}{45}) + 2 πn, A = - arccos (- \frac{11}{45}) + 2 πn

Show solutions in decimal form

A = 1.81774 \dots + 2 πn, A = - 1.81774 \dots + 2 πn

cos (x) = \frac{308}{1475}

tan (θ) = \frac{6}{3}

csc (θ) = - \frac{13}{5}

17 sin (θ + 61. 9^{\circ}) = k

cos (x) = 0.74

What is the general solution for 30^2=20^2+18^2-2(20)(18)cos(A) ?
The general solution for 30^2=20^2+18^2-2(20)(18)cos(A) is A=1.81774…+2pin,A=-1.81774…+2pin