Trigonometry Examples

$\sin (\tan (\frac{14 π}{3}))$

Step 1

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

$\sin (\tan (\frac{2 π}{3}))$

Step 2

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

$\sin (- \tan (\frac{π}{3}))$

Step 3

The exact value of $\tan (\frac{π}{3})$ is $\sqrt{3}$ .

$\sin (- \sqrt{3})$

Step 4

Since $\sin (- \sqrt{3})$ is an odd function, rewrite $\sin (- \sqrt{3})$ as $- \sin (\sqrt{3})$ .

$- \sin (\sqrt{3})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \sin (\sqrt{3})$

Decimal Form:

$- 0.98702664 \dots$