What is the general solution for sin(x)=0.75cos(x) ?

The general solution for sin(x)=0.75cos(x) is x=0.64350…+pin

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sin(x)=0.75cos(x)

sin (x) = 0.75 cos (x)

x = 0.64350 \dots + πn

Degrees

x = 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = 0.75 cos (x)

Rewrite using trig identities

sin (x) = 0.75 cos (x)

Divide both sides by

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

\frac{sin ( x )}{cos ( x )} = \frac{0.75 cos ( x )}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} = 0.75

Use the basic trigonometric identity:

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

tan (x) = 0.75

tan (x) = 0.75

Apply trig inverse properties

tan (x) = 0.75

General solutions for

tan (x) = 0.75

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

x = arctan (0.75) + πn

x = arctan (0.75) + πn

Show solutions in decimal form

x = 0.64350 \dots + πn

tan (x) = 1.15

0.6 = cos^{2} (x)

10 = 65 \cdot 5 \cdot cos (θ)

1 sin (4 0^{\circ}) = 1.5 sin (x)

4 sin^{2} (x) = 4 + cos (x)

What is the general solution for sin(x)=0.75cos(x) ?
The general solution for sin(x)=0.75cos(x) is x=0.64350…+pin