Given that tan theta=(1)/(3) and sin theta 0, what is cos theta?

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Given that  tan theta=(1)/(3) and  sin theta > 0, what is  cos theta?

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Given Information: We are given that tan theta = 1/3 and sin theta > 0. We need to find cos theta. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Since tan theta = 1/3, we can consider the opposite side to be 1 and the adjacent side to be 3 in a right triangle.Finding Opposite and Adjacent Sides: Using the Pythagorean theorem, we can find the hypotenuse of the triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Let's denote the hypotenuse as h. Then we have: h^2 = opposite^2 + adjacent^2 h^2 = 1^2 + 3^2 h^2 = 1 + 9 h^2 = 10 h = sqrt(10)Finding Hypotenuse: Now that we have the hypotenuse, we can find cos theta. The cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. cos theta = adjacent/hypotenuse cos theta = 3/sqrt(10)Finding Cosine: To rationalize the denominator, we multiply the numerator and the denominator by sqrt(10). cos theta = (3/sqrt(10)) * (sqrt(10)/sqrt(10)) cos theta = 3sqrt(10)/10

Given that $\tan \theta = \frac{1}{3}$ and \sin \theta > 0, what is $\cos \theta$ ?

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Given that $\tan \theta = \frac{1}{3}$ and \sin \theta > 0, what is $\cos \theta$ ?