Trigonometry: Tangent |
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Angles and sides in trigonometry: Tangent |
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Last but not the least is the trigonometric function called tangent. Look at the triangle above. Do you notice the following? * The unknown angle, α * The side adjacent to the unknown angle (15.3 in) * The side opposite to the unknown angle (6.37 in) We need the value of angle, α. Notice that the sides of the triangle are labeled appropriately 'adjacent side' and opposite' relative to the unknown angle α. To simplify our discussion, we will simply call the 'length of the adjacent side'simply the 'adjacent'. The other side will simply be referred to as ‘opposite’. The value for the tan of angle α is defined as the value that results when you divide the opposite side by the adjacent. The formula is written below: tan(α) = opposite / adjacent Or simply: tan(α) = opp / adj From the diagram above, we can easily solve the unknown angle with the tangent formula: tan(α) = 6.37 inches / 15.3 in tan(α) = 0.42 α = tan-1 0.42 α = 23° Note that the inverse sign is used above. This value can be found using your calculator. Remember: 1) If any two values i.e. the 2 sides or, an angle and a side, are given, the missing angle or side can always be found by simply substituting the correct values in the formula. 2) It always helps to draw the diagram to get an accurate picture of what’s being asked. 3) Use the calculator to enter the values of cosine and inverse cosine. Try the following questions
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Tuesday, April 8, 2014
Trigonometry Tangent
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