Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with $x = a \sin u$ or $x = a \tan u$ ? Why do we need to think about the unit circle after trigonometric substitution with $x = a s e c u$ ?

Question

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with $x = a \sin u$ or $x = a \tan u$ ? Why do we need to think about the unit circle after trigonometric substitution with $x = a s e c u$ ?

Accepted Answer

Ans: Quadrants came into account as the resultant absolute values are significant since $\tan u$ is positive for $u$ in the first quadrant and negative for $u$ in the second quadrant. That's why in this case unit circle is considered.

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with $x = a \sin u$ or $x = a \tan u$ ? Why do we need to think about the unit circle after trigonometric substitution with $x = a s e c u$ ?

Step by Step Solution

Step 1. Given information:

Step 2. Solving the trigonometric substitution:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with x = a sin u or x = a tan u? Why do we need to think about the unit circle after trigonometric substitution with x = a sec u?

Step by Step Solution

Step 1. Given information:

Step 2. Solving the trigonometric substitution:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Calculus

Pure Maths

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with $x = a \sin u$ or $x = a \tan u$ ? Why do we need to think about the unit circle after trigonometric substitution with $x = a s e c u$ ?