Question

find the signs of the six trigonometric function values for the given angle.
299°

sin 299° is ▼ cos 299° is ▼ and tan 299° is ▼

Explanation:

Step1: Determine the quadrant of \(299^\circ\)

Angles between \(270^\circ\) and \(360^\circ\) lie in the fourth quadrant. Since \(270^\circ< 299^\circ< 360^\circ\), \(299^\circ\) is in the fourth quadrant.

Step2: Recall the sign rules for trigonometric functions in each quadrant

• In the fourth quadrant:
• Sine function (\(\sin\)): The \(y\)-coordinate (which is related to \(\sin\)) is negative, so \(\sin\theta<0\) for \(\theta\) in the fourth quadrant.
• Cosine function (\(\cos\)): The \(x\)-coordinate (which is related to \(\cos\)) is positive, so \(\cos\theta > 0\) for \(\theta\) in the fourth quadrant.
• Tangent function (\(\tan\)): \(\tan\theta=\frac{\sin\theta}{\cos\theta}\), since \(\sin\theta<0\) and \(\cos\theta > 0\), \(\tan\theta=\frac{\text{negative}}{\text{positive}}=\text{negative}\), so \(\tan\theta<0\) for \(\theta\) in the fourth quadrant.

Answer:

\(\sin 299^\circ\) is negative, \(\cos 299^\circ\) is positive, and \(\tan 299^\circ\) is negative.