Trigonometry Examples

$\sin (2 \arctan (- 1))$

Step 1

The exact value of $\arctan (- 1)$ is $- \frac{π}{4}$ .

$\sin (2 (- \frac{π}{4}))$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Move the leading negative in $- \frac{π}{4}$ into the numerator.

$\sin (2 \frac{- π}{4})$

Step 2.2

Factor $2$ out of $4$ .

$\sin (2 \frac{- π}{2 (2)})$

Step 2.3

Cancel the common factor.

$\sin (2 \frac{- π}{2 \cdot 2})$

Step 2.4

Rewrite the expression.

$\sin (\frac{- π}{2})$

Step 3

Move the negative in front of the fraction.

$\sin (- \frac{π}{2})$

Step 4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{3 π}{2})$

Step 5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$- \sin (\frac{π}{2})$

Step 6

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$- 1 \cdot 1$

Step 7

Multiply $- 1$ by $1$ .

$- 1$