Question

find the signs of the six trigonometric function values for the given angle.
88°

sin 88° is ▼ cos 88° is ▼ and tan 88° is ▼

Explanation:

Step1: Determine the quadrant of \(88^\circ\)

Angles between \(0^\circ\) and \(90^\circ\) lie in the first quadrant. Since \(0^\circ< 88^\circ< 90^\circ\), \(88^\circ\) is in the first quadrant.

Step2: Recall the sign rules in the first quadrant

In the first quadrant, all trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) are positive. For sine, cosine, and tangent specifically:

• The sine function (\(\sin\theta\)) in the first quadrant: \(y\)-coordinate (opposite side in right triangle or \(y\) in unit circle) is positive, so \(\sin\theta> 0\) for \(\theta\) in first quadrant.
• The cosine function (\(\cos\theta\)) in the first quadrant: \(x\)-coordinate (adjacent side in right triangle or \(x\) in unit circle) is positive, so \(\cos\theta> 0\) for \(\theta\) in first quadrant.
• The tangent function (\(\tan\theta=\frac{\sin\theta}{\cos\theta}\)), since both \(\sin\theta\) and \(\cos\theta\) are positive in the first quadrant, their ratio is also positive, so \(\tan\theta > 0\) for \(\theta\) in first quadrant.

Answer:

\(\sin 88^\circ\) is positive, \(\cos 88^\circ\) is positive, and \(\tan 88^\circ\) is positive.