What is the general solution for 10cos(x)=2.5sin(x) ?

The general solution for 10cos(x)=2.5sin(x) is x=1.32581…+pin

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Popular >

10cos(x)=2.5sin(x)

Solution

10 cos (x) = 2.5 sin (x)

Solution

x = 1.32581 \dots + πn

Degrees

x = 75.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

10 cos (x) = 2.5 sin (x)

Rewrite using trig identities

10 cos (x) = 2.5 sin (x)

Divide both sides by

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

\frac{10 cos ( x )}{cos ( x )} = \frac{2.5 sin ( x )}{cos ( x )}

Simplify

10 = \frac{2.5 sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

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

10 = 2.5 tan (x)

Switch sides

2.5 tan (x) = 10

2.5 tan (x) = 10

Multiply both sides by

10

2.5 tan (x) = 10

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

2.5 tan (x) \cdot 10 = 10 \cdot 10

Refine

25 tan (x) = 100

25 tan (x) = 100

Divide both sides by

25

25 tan (x) = 100

Divide both sides by

25

\frac{25 tan ( x )}{25} = \frac{100}{25}

Simplify

tan (x) = 4

tan (x) = 4

Apply trig inverse properties

tan (x) = 4

General solutions for

tan (x) = 4

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

x = arctan (4) + πn

x = arctan (4) + πn

Show solutions in decimal form

x = 1.32581 \dots + πn

Popular Examples

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sin (0.6) - sin (0.6 + x) = 0.95

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tan (x) = \frac{56}{91}

solvefor x,tan(x)=cot(x)solve for

x, tan (x) = cot (x)

arccos(x)= 5/6

arccos (x) = \frac{5}{6}

5cos(x)=-2sin^2(x)+4,0<= x<= 2pi

5 cos (x) = - 2 sin^{2} (x) + 4, 0 \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for 10cos(x)=2.5sin(x) ?
The general solution for 10cos(x)=2.5sin(x) is x=1.32581…+pin