What is the general solution for 0=-6(sin(t))+7(cos(t)) ?

The general solution for 0=-6(sin(t))+7(cos(t)) is t=0.86217…+pin

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0=-6(sin(t))+7(cos(t))

0 = - 6 (sin (t)) + 7 (cos (t))

t = 0.86217 \dots + πn

Degrees

t = 49.39870 \dots^{\circ} + 18 0^{\circ} n

Solution steps

0 = - 6 (sin (t)) + 7 (cos (t))

Switch sides

- 6 sin (t) + 7 cos (t) = 0

Rewrite using trig identities

- 6 sin (t) + 7 cos (t) = 0

Divide both sides by

cos (t), cos (t) \neq = 0

\frac{- 6 sin ( t ) + 7 cos ( t )}{cos ( t )} = \frac{0}{cos ( t )}

Simplify

- \frac{6 sin ( t )}{cos ( t )} + 7 = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

- 6 tan (t) + 7 = 0

- 6 tan (t) + 7 = 0

Move

7

to the right side

- 6 tan (t) + 7 = 0

Subtract

7

from both sides

- 6 tan (t) + 7 - 7 = 0 - 7

Simplify

- 6 tan (t) = - 7

- 6 tan (t) = - 7

Divide both sides by

- 6

- 6 tan (t) = - 7

Divide both sides by

- 6

\frac{- 6 tan ( t )}{- 6} = \frac{- 7}{- 6}

Simplify

tan (t) = \frac{7}{6}

tan (t) = \frac{7}{6}

Apply trig inverse properties

tan (t) = \frac{7}{6}

General solutions for

tan (t) = \frac{7}{6}

tan (x) = a \Rightarrow x = arctan (a) + πn

t = arctan (\frac{7}{6}) + πn

t = arctan (\frac{7}{6}) + πn

Show solutions in decimal form

t = 0.86217 \dots + πn

sec (θ) - 2 = 0, 0 \leq θ \leq 2 π

1 + cot^{2} (x) = csc (x)

cos (θ) = \frac{7}{3 17}

sin (A) - 0.1 \cdot cos (A) = \frac{6.94}{9.8}

t, s = 2 arctan (t)

What is the general solution for 0=-6(sin(t))+7(cos(t)) ?
The general solution for 0=-6(sin(t))+7(cos(t)) is t=0.86217…+pin