SOLUTION: The terminal side of angle theta in standard position lies on the given line in the given quadrant. Find sin theta, cos theta and tan theta.
2x + 3y=0; quadrant IV
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2x + 3y=0; quadrant IV
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Question 231164: The terminal side of angle theta in standard position lies on the given line in the given quadrant. Find sin theta, cos theta and tan theta.
2x + 3y=0; quadrant IV Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! In the fourth quadrant, x's are positive and y's are negative. So let's find a point on the line in the fourth quadrant by picking a positive value for x and the using the equation to find the corresponding y. To avoid fractions, I'm going to pick 3 for x:
2(3) + 3y = 0
6 + 3y = 0
3y = -6
y = -2
Here's a drawing of what we have so far:
We already have what we need for tan. But we need the hypotenuse for the sin and cos. We'll use the Pythagorean Theorem for this:
Now we can find our values. (Since Algebra.com's formula software does not "do" theta, for some unknown reason, I'll use x instead):
We don't usually leave square roots in denominators so we'll rationalize the sin and cos:
(