What is the general solution for sin(30-x)+cos(x)=0 ?

The general solution for sin(30-x)+cos(x)=0 is x=60+180n

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sin(30-x)+cos(x)=0

sin (3 0^{\circ} - x) + cos (x) = 0

x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

sin (3 0^{\circ} - x) + cos (x) = 0

Rewrite using trig identities

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) = 0

Simplify

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) : \frac{3 cos ( x ) - 3 sin ( x )}{2}

\frac{3 cos ( x ) - 3 sin ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 cos (x) - 3 sin (x) = 0

Rewrite using trig identities

3 - 3 tan (x) = 0

Move

3

to the right side

- 3 tan (x) = - 3

Divide both sides by

- 3

tan (x) = 3

General solutions for

tan (x) = 3

x = 6 0^{\circ} + 18 0^{\circ} n

tan (b x) = 5

sin (t + \frac{π}{4}) = \frac{1}{2}, π \leq t \leq \frac{7 π}{2}

tan (x) = 3007

2 sin (θ) - 3 = 0

2 cos^{2} (t) + 7 cos (t) + 5 = 0

What is the general solution for sin(30-x)+cos(x)=0 ?
The general solution for sin(30-x)+cos(x)=0 is x=60+180n