How to Find the Sine, Cosine and Tangent of an Angle
Sine, cosine and tangent are the three most basic identities of trigonometry. Using them requires understanding the relationships between the angles and sides of a triangle. Given the unknown angle theta, you can identify the three sides of the triangle using the terms adjacent, opposite and hypotenuse. The opposite side is the one opposite to theta, the one adjacent is the shorter adjacent side and the hypotenuse is the longer adjacent side. Using this knowledge, you can then solve for the sine, cosine and tangent of theta.
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Instructions
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Calculate the sine of unknown angle theta by dividing the opposite side (opp) by the hypotenuse side (hyp). Thus, the sine of theta = opp/hyp. Given an opposite side of 1 inch and a hypotenuse of 2 inches, the sine of theta would be 1/2, or 0.5.
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Divide the side adjacent (adj) to the unknown angle theta by the hypotenuse side (hyp) to determine the cosine of theta. Thus, the cosine of theta = adj/hyp. Given an adjacent value of 4 inches and a hypotenuse of 5.65 inches, the cosine of theta would be 4/5.65, or 0.708.
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Calculate the tangent of unknown angle theta by dividing the side opposite (opp) to it by the side adjacent (adj) to it. Thus, the tangent of opp/adj. Given an opposite value of 2 inches and an opposite value of 2 inches, the tangent of theta would be 2/2, or 1.00.
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