Expand Using Sum/Difference Formulas cos((2pi)/3)

$\cos (\frac{2 π}{3})$

The angle $\frac{2 π}{3}$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\cos (\frac{2 π}{3} + 0)$

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

$\cos (0) \cdot \cos (\frac{2 π}{3}) - \sin (0) \cdot \sin (\frac{2 π}{3})$

The exact value of $\cos (0)$ is $1$ .

$(1) \cdot \cos (\frac{2 π}{3}) - \sin (0) \cdot \sin (\frac{2 π}{3})$

Simplify $\cos (\frac{2 π}{3})$ .

Tap for more steps...

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

$(1) \cdot (- \cos (\frac{π}{3})) - \sin (0) \cdot \sin (\frac{2 π}{3})$

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$(1) \cdot (- \frac{1}{2}) - \sin (0) \cdot \sin (\frac{2 π}{3})$

The exact value of $\sin (0)$ is $0$ .

$(1) \cdot (- \frac{1}{2}) + 0 \cdot \sin (\frac{2 π}{3})$

Simplify $\sin (\frac{2 π}{3})$ .

Tap for more steps...

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$(1) \cdot (- \frac{1}{2}) + 0 \cdot \sin (\frac{π}{3})$

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$(1) \cdot (- \frac{1}{2}) + 0 \cdot \frac{\sqrt{3}}{2}$

Simplify each term.

Tap for more steps...

Multiply $- \frac{1}{2}$ by $1$ .

$- \frac{1}{2} + 0 \cdot \frac{\sqrt{3}}{2}$

Multiply $0$ by $\frac{\sqrt{3}}{2}$ .

$- \frac{1}{2} + 0$

Add $- \frac{1}{2}$ and $0$ .

$- \frac{1}{2}$

Do you know how to Expand Using Sum/Difference Formulas cos((2pi)/3)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Determine the Type of Number tan(0)csc(0)

Find the Exact Value tan(arccos(-15/17))

Graph y=2cos(x-pi/2)-1

Find the Exact Value sin(7/25)

Solve the Triangle a=12 , b=11 , A=35