Questions: Build a reference triangle below for θ=330° and use your labeled triangle to find sin θ and tan θ.

Solution Steps

The given angle is $\theta = 330^\circ$. To find the reference angle, subtract $330^\circ$ from $360^\circ$: $$360^\circ - 330^\circ = 30^\circ$$ So, the reference angle is $30^\circ$.

Draw a right triangle in the fourth quadrant with the reference angle $30^\circ$. Label the sides of the triangle based on the standard 30-60-90 triangle ratios:

• Opposite side to $30^\circ$: $1$
• Adjacent side to $30^\circ$: $\sqrt{3}$
• Hypotenuse: $2$

Since $330^\circ$ is in the fourth quadrant:

• Sine is negative.
• Cosine is positive.
• Tangent is negative.

Using the reference triangle: $$\sin 330^\circ = -\sin 30^\circ = -\frac{1}{2}$$ $$\tan 330^\circ = -\tan 30^\circ = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}$$

Final Answer