Given that sin^2x = 4/13, what is the cos^2x?
I am so lost. I need to show my work. Please help.
THANK YOU!
if sin^2 x = 4/13
sin x = ± 2/√13
telling me that x could in any of the 4 quadrants
using the first quadrant triangle
x^2 + 2^2 = √13^2
x^2 = 9
cos^2 = x^2/r^2 = 9/13
or, in a shorter way:
we know : sin^2 x + cos^2 x = 1
cos^2 x + 4/13 = 1
cos^2 x = 1-4/13 = 9/13
Well, well, well, if it isn't another victim of the trigonometric funhouse! Don't worry, my friend, I'll help guide you through this maze of sine and cosine.
First things first, we know that sin^2x = 4/13. Now, since we're talking about squares, we can make use of the Pythagorean identity: sin^2x + cos^2x = 1. Fancy, huh?
So, let's plug in our known value for sin^2x: 4/13 + cos^2x = 1. Now, all we need to do is isolate that cheeky little cos^2x.
Subtract 4/13 from both sides: cos^2x = 1 - 4/13. Simplify, simplify, simplify, and we get cos^2x = 9/13. Ta-da!
So, after our little journey through the trigonometric funhouse, we've found that cos^2x = 9/13. Mission accomplished, my friend! High five! *virtual high-five*
To find the value of cos^2x, you can use the Pythagorean identity for trigonometric functions. The Pythagorean identity states that sin^2x + cos^2x = 1.
Given that sin^2x = 4/13, we can substitute this value into the Pythagorean identity equation:
4/13 + cos^2x = 1
To solve for cos^2x, we need to isolate it on one side of the equation. Subtract 4/13 from both sides:
cos^2x = 1 - 4/13
Find a common denominator to subtract the fractions:
cos^2x = 13/13 - 4/13
cos^2x = 9/13
So, cos^2x = 9/13.
To find the value of cos^2x, we can use the Pythagorean identity: sin^2x + cos^2x = 1. Rearranging this equation, we get cos^2x = 1 - sin^2x.
Given sin^2x = 4/13, we can substitute this into the equation to find cos^2x.
cos^2x = 1 - sin^2x
cos^2x = 1 - 4/13
cos^2x = 13/13 - 4/13
cos^2x = 9/13
Therefore, the value of cos^2x is 9/13.
To show your work, you need to include the steps I mentioned above. Make sure to clearly state the equation (sin^2x + cos^2x = 1), substitute the given value (sin^2x = 4/13), and show the calculations step by step until you arrive at cos^2x = 9/13.