III. Solve for the value of x using a scientific calculator and round of your answer to whole number. Ex. \( \tan x=\frac{16}{21} \) SOLUTION: \( \tan x=\frac{16}{21} \quad \rightarrow \) take the inverse of tan. This is usually labeled as \( \tan ^{-1} \) or atan \( x=\tan ^{-1}\left(\frac{16}{21}\right) \quad \rightarrow \) divide 16 by 21 to get the decimal form 0.7619 \( \mathrm{x}=\tan ^{-1}(0.7619) \rightarrow \) type this on your scientific calculator and round off your answer to whole number \( \mathrm{x}=37^{\circ} \) 11. \( \cos x=\frac{4}{5} \) 14. \( \sin x=\frac{12}{17} \) 12. \( \sin x=\frac{2}{5} \) 15. \( \tan x=\frac{13}{25} \) 13. \( \tan x=\frac{7}{5} \) 16. \( \cos x=\frac{8}{15} \)

Did you know that the tangent, sine, and cosine functions are fundamental in the world of trigonometry? These ratios arise from the relationships between the angles and sides of right triangles and are crucial for various fields like physics, engineering, and architecture. That's right! Architects rely on these functions to ensure their designs are not just beautiful but also structurally sound. However, beware of common pitfalls when using trigonometric functions! One frequent mistake is mixing up the ratios or using the wrong inverse function. Always double-check your calculator modes—ensure it's set to degrees if you're looking for degree measures, otherwise you might end up with results in radians and a lot of confusion!