What is the general solution for 8^2=17^2+15^2-2(17)(15)cos(A) ?

The general solution for 8^2=17^2+15^2-2(17)(15)cos(A) is A=0.48995…+2pin,A=2pi-0.48995…+2pin

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8^2=17^2+15^2-2(17)(15)cos(A)

8^{2} = 1 7^{2} + 1 5^{2} - 2 (17) (15) cos (A)

A = 0.48995 \dots + 2 πn, A = 2 π - 0.48995 \dots + 2 πn

Degrees

A = 28.07248 \dots^{\circ} + 36 0^{\circ} n, A = 331.92751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

8^{2} = 1 7^{2} + 1 5^{2} - 2 (17) (15) cos (A)

Switch sides

1 7^{2} + 1 5^{2} - 2 \cdot 17 \cdot 15 cos (A) = 8^{2}

Multiply the numbers:

2 \cdot 17 \cdot 15 = 510

1 7^{2} + 1 5^{2} - 510 cos (A) = 8^{2}

1 7^{2} = 289

289 + 1 5^{2} - 510 cos (A) = 8^{2}

1 5^{2} = 225

289 + 225 - 510 cos (A) = 8^{2}

Add the numbers:

289 + 225 = 514

- 510 cos (A) + 514 = 8^{2}

8^{2} = 64

- 510 cos (A) + 514 = 64

Move

514

to the right side

- 510 cos (A) + 514 = 64

Subtract

514

from both sides

- 510 cos (A) + 514 - 514 = 64 - 514

Simplify

- 510 cos (A) = - 450

- 510 cos (A) = - 450

Divide both sides by

- 510

- 510 cos (A) = - 450

Divide both sides by

- 510

\frac{- 510 cos ( A )}{- 510} = \frac{- 450}{- 510}

Simplify

\frac{- 510 cos ( A )}{- 510} = \frac{- 450}{- 510}

Simplify

\frac{- 510 cos ( A )}{- 510} : cos (A)

\frac{- 510 cos ( A )}{- 510}

Apply the fraction rule:

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

= \frac{510 cos ( A )}{510}

Divide the numbers:

\frac{510}{510} = 1

= cos (A)

Simplify

\frac{- 450}{- 510} : \frac{15}{17}

\frac{- 450}{- 510}

Apply the fraction rule:

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

= \frac{450}{510}

Cancel the common factor:

30

= \frac{15}{17}

cos (A) = \frac{15}{17}

cos (A) = \frac{15}{17}

cos (A) = \frac{15}{17}

Apply trig inverse properties

cos (A) = \frac{15}{17}

General solutions for

cos (A) = \frac{15}{17}

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

A = arccos (\frac{15}{17}) + 2 πn, A = 2 π - arccos (\frac{15}{17}) + 2 πn

A = arccos (\frac{15}{17}) + 2 πn, A = 2 π - arccos (\frac{15}{17}) + 2 πn

Show solutions in decimal form

A = 0.48995 \dots + 2 πn, A = 2 π - 0.48995 \dots + 2 πn

2 cos^{2} (t) = sin^{2} (t)

5 sin (θ) + 3 = 3

sin (3 x) = 0, 0 < x \leq 2

tan (x) = - 0.35

0 = cos (2 t - \frac{π}{3})

What is the general solution for 8^2=17^2+15^2-2(17)(15)cos(A) ?
The general solution for 8^2=17^2+15^2-2(17)(15)cos(A) is A=0.48995…+2pin,A=2pi-0.48995…+2pin