Math Problem Statement

0=tan^-1(0.29)

Solution

The equation 0=tan1(0.29)0 = \tan^{-1}(0.29) is asking for the angle whose tangent is 0.29.

However, tan1(x)\tan^{-1}(x) refers to the inverse tangent function (also called arctangent), which is used to find the angle corresponding to a given tangent value.

Let's break it down:

  • tan1(0.29)\tan^{-1}(0.29) is the angle θ\theta such that: tan(θ)=0.29\tan(\theta) = 0.29

This implies the value of θ\theta is a positive angle, not zero. The value of tan1(0.29)\tan^{-1}(0.29) would give a specific angle, but it's not zero.

To find this angle, we compute:

θ=tan1(0.29)\theta = \tan^{-1}(0.29)

Using a calculator or mathematical software:

θ16.26\theta \approx 16.26^\circ

Thus, the equation 0=tan1(0.29)0 = \tan^{-1}(0.29) does not hold true, since tan1(0.29)\tan^{-1}(0.29) is approximately 16.2616.26^\circ, not zero.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Inverse Trigonometric Functions
Arctangent

Formulas

tan^-1(x) = θ
tan(θ) = x

Theorems

Inverse tangent theorem

Suitable Grade Level

Grades 9-12