verify solutions

Question

Verify that her solutions are correct

Latoya determined two approximate solutions to the equation 3 + sin2 x = tan2 x + 1 to be these:
x = 1.027 and x = 2.281. Verify that her solutions are correct. Explain your reasoning

Answer 1

The way to verify whether these solutions are correct is to take the given values and plug them into the original equation. This will turn them into:

 

1. 3+sin(2*1.027)=tan(2*1.027)+1

2. 3+sin(2*2.281)=tan(2*2.281)+1

 

Then you perform the calculations to get numerical answers for the left and right side of the equations. If both sides of the equations agree, then those answers (x=1.027 and x=2.281) are correct!

 

This is a technique that is useful for all sorts of problems in math and science as well. If you are told to solve an algreba problem for instance, you can solve it. If you are unsure of your answer, you can plug it into the original equation to see if the equation is true.