Question

evaluate the sine, cosine, and tangent of the angle without using a calculator. (if an answer is undefined, enter undefined.) -840° sin θ = cos θ = tan θ = resources watch it master it ebook submit answer

Explanation:

Step1: Find a coterminal angle

Add \(360^{\circ}\) multiple - times to \(- 840^{\circ}\) to get a positive coterminal angle. \(-840^{\circ}+3\times360^{\circ}=-840^{\circ} + 1080^{\circ}=240^{\circ}\).

Step2: Recall the unit - circle values for \(240^{\circ}\)

The coordinates of the point on the unit - circle corresponding to an angle \(\theta = 240^{\circ}\) are \((\cos\theta,\sin\theta)\). For \(\theta = 240^{\circ}\), \(\sin\theta=-\frac{\sqrt{3}}{2}\), \(\cos\theta=-\frac{1}{2}\).

Step3: Calculate the tangent

Use the formula \(\tan\theta=\frac{\sin\theta}{\cos\theta}\). Substitute \(\sin\theta = -\frac{\sqrt{3}}{2}\) and \(\cos\theta=-\frac{1}{2}\), then \(\tan\theta=\frac{-\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=\sqrt{3}\).

Answer:

\(\sin\theta = -\frac{\sqrt{3}}{2}\)
\(\cos\theta=-\frac{1}{2}\)
\(\tan\theta=\sqrt{3}\)