Sarah used her calculator to find sin125 degree. She wrote down sin125 degrees = -.57. How could Sarah recognize that her answer is incorrect?
Sarah is wrong because her answer is for Cos(125) not Sin(125... Sin(125) equals .81915204
To recognize that her answer is incorrect, Sarah should compare her answer to the correct value of sin(125 degrees).
1. Sarah should first check the range of the sine function. The range of sine is between -1 and 1, inclusive. If Sarah's answer, in this case, is outside this range, it is definitely incorrect.
2. Sarah can use a scientific calculator or an online tool to find the accurate value of sin(125 degrees). She can type in "sin(125)" in degrees mode, and the calculator will provide the correct result.
3. Once she has the correct value, she can compare it with her answer. If they are different, then Sarah's answer is incorrect.
In this case, Sarah's answer of sin125 degrees = -0.57 is incorrect because the correct value of sin(125 degrees) is approximately 0.82. So, Sarah can recognize that her answer is incorrect by comparing it with the correct value.
To determine if Sarah's answer of sin125 degrees = -.57 is incorrect, she can compare it to the correct value or use the properties of the sine function. Here's how she can do that:
1. Check with a reference: Sarah can verify her answer by referencing a table of trigonometric values or using a reliable calculator or trigonometric software. The correct value of sin125 degrees is approximately 0.819, not -0.57. By comparing her answer to the correct value, Sarah can confirm that her answer is incorrect.
2. Understand the properties of the sine function: The sine function is periodic with a period of 360 degrees (or 2π radians). This means that if Sarah adds or subtracts multiples of the period from 125 degrees, she will get the same value. For example, sin125 degrees is equivalent to sin(125 + 360n) degrees, where "n" is an integer. Therefore, Sarah can try adding or subtracting multiples of 360 degrees to 125 degrees and check if the sine value matches her answer. If the values do not match, then she knows that her answer is incorrect.
Additionally, Sarah can review her approach to calculating sin125 degrees to identify any potential mistakes, such as inputting the wrong number into the calculator or using incorrect units. Double-checking the input and calculations will help her identify and rectify any errors.