What is the general solution for 7.5sin(x)=3.4cos(x) ?

The general solution for 7.5sin(x)=3.4cos(x) is x=0.42562…+pin

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Popular >

7.5sin(x)=3.4cos(x)

Solution

7.5 sin (x) = 3.4 cos (x)

Solution

x = 0.42562 \dots + πn

Degrees

x = 24.38637 \dots^{\circ} + 18 0^{\circ} n

Solution steps

7.5 sin (x) = 3.4 cos (x)

Rewrite using trig identities

7.5 sin (x) = 3.4 cos (x)

Divide both sides by

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

\frac{7.5 sin ( x )}{cos ( x )} = \frac{3.4 cos ( x )}{cos ( x )}

Simplify

\frac{7.5 sin ( x )}{cos ( x )} = 3.4

Use the basic trigonometric identity:

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

7.5 tan (x) = 3.4

7.5 tan (x) = 3.4

Multiply both sides by

10

7.5 tan (x) = 3.4

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

7.5 tan (x) \cdot 10 = 3.4 \cdot 10

Refine

75 tan (x) = 34

75 tan (x) = 34

Divide both sides by

75

75 tan (x) = 34

Divide both sides by

75

\frac{75 tan ( x )}{75} = \frac{34}{75}

Simplify

tan (x) = \frac{34}{75}

tan (x) = \frac{34}{75}

Apply trig inverse properties

tan (x) = \frac{34}{75}

General solutions for

tan (x) = \frac{34}{75}

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

x = arctan (\frac{34}{75}) + πn

x = arctan (\frac{34}{75}) + πn

Show solutions in decimal form

x = 0.42562 \dots + πn

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Frequently Asked Questions (FAQ)

What is the general solution for 7.5sin(x)=3.4cos(x) ?
The general solution for 7.5sin(x)=3.4cos(x) is x=0.42562…+pin