Purchase Solution

Inverse Trigonometric Functions

Not what you're looking for?

Ask Custom Question

Find the exact value of the expression(Consider interval is [0,pi]

I)
1) sin^-1 SQRT3 / 2 = pi/3
2) arctan(-1) = 3pi / 4
3) csc^-1 2 = pi/6
4) sec^-1 SQRT(2) = pi/4

II) We were given the example to derive sin^-1x as follows.

y=sin^-1 (x)
siny = x
(cosy)(dy/dx) = 1
(dy/dx) = 1/cosy = 1 / (SQRT(1-sin^2 (y))
= 1 / SQRT(1-x^2) (-pi/2 < y < pi/2)

NOW, please follow the same steps, but now derive cos^-1 (x) and then cot^-1 (x).

Purchase this Solution

Solution Summary

The solution gives a step-by-step procedure to solve a couple of problems related to inverse functions.

Solution Preview

Here are the solutions to the problems given.

1) As we know that sin60 = sqrt(3/2) = sin(pi/3)

Substituting the value of sqrt(3/2)

Left Hand Side = sin^-1sin(pi/3)

= pi/3

2) We know that tan(3pi/4) = -1 = ...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts