Find each exact function value. See Example 3.
sin π/2

Guida verificata passo dopo passo

Recall that the sine function, \( \sin \theta \), gives the y-coordinate of the point on the unit circle corresponding to the angle \( \theta \).

Identify the angle given: \( \frac{\pi}{2} \) radians, which corresponds to 90 degrees.

Visualize or recall the unit circle: at \( \frac{\pi}{2} \), the point on the unit circle is at the top, with coordinates \( (0, 1) \).

Since sine corresponds to the y-coordinate, \( \sin \frac{\pi}{2} = 1 \).

Therefore, the exact value of \( \sin \frac{\pi}{2} \) is 1.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Unit Circle and Radian Measure

The unit circle is a circle with radius 1 centered at the origin of the coordinate plane. Angles measured in radians correspond to points on this circle, where π radians equal 180 degrees. Understanding the unit circle helps in finding exact trigonometric values for common angles like π/2.

Video consigliato:

Percorso guidato

06:11

Introduction to the Unit Circle

Sine Function Definition

The sine of an angle in the unit circle is the y-coordinate of the corresponding point on the circle. For an angle θ, sin(θ) gives the vertical position on the unit circle, which allows exact evaluation of sine values at standard angles such as π/2.

Video consigliato:

Percorso guidato

5:53

Graph of Sine and Cosine Function

Exact Values of Trigonometric Functions at Special Angles

Certain angles like 0, π/6, π/4, π/3, and π/2 have well-known exact sine and cosine values. For example, sin(π/2) equals 1. Memorizing these exact values avoids approximation and is essential for solving trigonometric problems precisely.

Video consigliato:

Percorso guidato