Trigonometry Examples

$\sin (a) = \cos (x)$

Step 1

Solve the equation for $a$ .

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Step 1.1

Rewrite the equation as $\cos (x) = \sin (a)$ .

$\cos (x) = \sin (a)$

Step 1.2

Take the inverse cosine of both sides of the equation to extract $a$ from inside the cosine.

$x = \arccos (\sin (a))$

Step 1.3

Rewrite the equation as $\arccos (\sin (a)) = x$ .

$\arccos (\sin (a)) = x$

Step 1.4

Take the inverse arccosine of both sides of the equation to extract $\sin (a)$ from inside the arccosine.

$\sin (a) = \cos (x)$

Step 1.5

Take the inverse sine of both sides of the equation to extract $a$ from inside the sine.

$a = \arcsin (\cos (x))$

Step 1.6

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\arccos (\sin (a)) = x$

Step 1.7

Take the inverse arccosine of both sides of the equation to extract $\sin (a)$ from inside the arccosine.

$\sin (a) = \cos (x)$

Step 1.8

Take the inverse sine of both sides of the equation to extract $a$ from inside the sine.

$a = \arcsin (\cos (x))$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $a$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear