How to Calculate the Sin of pi/2 Using a Scientific Calculator

The sine of π/2 is a fundamental value in trigonometry, and it has a precise value of 1. This tutorial will guide you through the process of calculating this value using a scientific calculator.

Understanding the Basics

The sine function, often denoted as sin, is a trigonometric function that provides the y-coordinate of a point on the unit circle. The angle π/2 radians corresponds to 90 degrees, and the sine of 90 degrees is 1.

Using a Scientific Calculator

To calculate sin(π/2) using a scientific calculator, follow these steps:

Turn on your calculator: Ensure that the calculator is in standard mode. Set the angle mode: Since the angle is in radians, change the calculator to radians mode. This setting can usually be found in the settings or mode menu. Enter the value: Enter π/2. Many calculators have a dedicated π button, so you can enter it directly. Calculate the sine: Press the sin button after entering π/2. Read the result: The display should show the value 1.

So, sin(π/2) 1.

Common Misinterpretations

The question may seem ambiguous due to the lack of parentheses. Here are some common interpretations:

sin(π/2) (Correct): The sine of π/2 radians is 1. (sin π)/2 (Incorrect): This would be equivalent to dividing the sine of π by 2, which is 0 because sin(π) 0. sin(π/2) in degrees (Incorrect): If π/2 is interpreted as degrees, then sin(90°) 1.

Standard Angles in Trigonometry

Standard angles such as π/6 (30°), π/3 (60°), and π/2 (90°) have special sine values that are commonly used. The sine of π/2 is 1, and this value is automatically known for many trigonometric problems. However, if you need to calculate it using a scientific calculator, the steps are straightforward.

Example Calculation

To find the sine of π/2:

Set the mode to radians. Type sin(π/2). The answer will be 1.

Alternatively, if you are working in degrees:

Change the angle mode to degrees. Type 90. Press the sin button. The answer will be 1.

Conclusion

The sine of π/2 is a fundamental trigonometric value that equals 1. By following a few simple steps, you can easily calculate this value using a scientific calculator. Understanding these basic trigonometric values is essential for solving more complex trigonometric problems.