What is the general solution for 8cos(a)-15sin(a)=0 ?

The general solution for 8cos(a)-15sin(a)=0 is a=0.48995…+pin

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8cos(a)-15sin(a)=0

8 cos (a) - 15 sin (a) = 0

a = 0.48995 \dots + πn

Degrees

a = 28.07248 \dots^{\circ} + 18 0^{\circ} n

Solution steps

8 cos (a) - 15 sin (a) = 0

Rewrite using trig identities

8 cos (a) - 15 sin (a) = 0

Divide both sides by

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

\frac{8 cos ( a ) - 15 sin ( a )}{cos ( a )} = \frac{0}{cos ( a )}

Simplify

8 - \frac{15 sin ( a )}{cos ( a )} = 0

Use the basic trigonometric identity:

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

8 - 15 tan (a) = 0

8 - 15 tan (a) = 0

Move

8

to the right side

8 - 15 tan (a) = 0

Subtract

8

from both sides

8 - 15 tan (a) - 8 = 0 - 8

Simplify

- 15 tan (a) = - 8

- 15 tan (a) = - 8

Divide both sides by

- 15

- 15 tan (a) = - 8

Divide both sides by

- 15

\frac{- 15 tan ( a )}{- 15} = \frac{- 8}{- 15}

Simplify

tan (a) = \frac{8}{15}

tan (a) = \frac{8}{15}

Apply trig inverse properties

tan (a) = \frac{8}{15}

General solutions for

tan (a) = \frac{8}{15}

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

a = arctan (\frac{8}{15}) + πn

a = arctan (\frac{8}{15}) + πn

Show solutions in decimal form

a = 0.48995 \dots + πn

tan (t) = \frac{3}{tan ( t )}

tan (- x) = tan (2 x + 1)

(2 cos (x) - sin (x)) (1 + sin (x)) = cos^{2} (x)

sin (6 x) cos (9 x) - cos (6 x) sin (9 x) = - 0.4

sin^{2} (x) = 2 tan^{2} (x)

What is the general solution for 8cos(a)-15sin(a)=0 ?
The general solution for 8cos(a)-15sin(a)=0 is a=0.48995…+pin