Find cos theta if sin theta = 3/5 and 90 degrees<theta<180 degrees.
Is the answer -sqrt34/5?
Appreciate you checking my anwers.
cos is - in second quadrant
this is a 3,4,5 right triangle but anyway
3^2 + x^2 = 25
x^2 = 16
x = 4 but actually -4 because in quadrant 2
cos t = -4/5
To find the value of cos(theta), we will use the Pythagorean identity for trigonometric functions.
We know that sin(theta) = 3/5. Since theta is in the second quadrant (90 degrees < theta < 180 degrees), sin(theta) is positive.
Using the Pythagorean identity, we have:
cos(theta) = √(1 - sin^2(theta))
Substituting sin(theta) = 3/5, we get:
cos(theta) = √(1 - (3/5)^2)
cos(theta) = √(1 - 9/25)
cos(theta) = √(16/25)
cos(theta) = 4/5
So, the correct answer is 4/5, not -√34/5.
Please note that when sin(theta) is positive, cos(theta) is also positive in the second quadrant. It is always good to double-check your calculations and make sure that you consider the correct quadrant while finding trigonometric values.