Each of the trigonometric functions sine, cosine, tangent, secant, cosecant and cotangent has an inverse (with a restricted domain). The inverse is used khổng lồ obtain the measure of an angle using the ratios from basic right triangle trigonometry. The inverse of tangent is denoted as
Arctangent or on a calculator it will appear as
atan or
tan-1. Note: this does NOT mean tangent raised to the negative one power.
Let"s look at an example of how khổng lồ use the inverse tangent function lớn find the measure of an angle in a right triangle. (triangle not drawn lớn scale)To find the measure in degrees of angle A using the tangent inverse, recall that Use a scientific calculator *Make sure your calculator is in degree mode30° = ALet"s look at an application problem.Squeaky Squirrel is 6 feet from the base of a tree that is 10 feet tall. What is the angle of elevation as Squeaky looks at the đứng top of the tree? Begin by creating a diagram of the given information. Recall that tangentθ = Therefore tangentθ = Use the inverse of tangent rounded to lớn the nearest tenthIf it is understood how to lớn use the basic right triangle trigonometric ratios, then the inverse can be used khổng lồ find a missing angle measure in any right triangle.
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If all three sides of the triangle are given then any of the trig ratios can be used và an equivalent angle measure will be derived. Sine, cosine, secant, tangent, cosecant & cotangent are all functions however, the inverses are only a function when given a restricted domain.
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