**INVERSE TRIGONOMETRIC FUNCTIONS**

Example 1:

Using a calculator, find

in degrees and radians rounded to two decimal places.sin^{ }^{ -1}(0.86)You access

by first pressing the "2nd" or "Shift" key on your calculator and then pressing the "sin" key.sin^{ }^{ -1}If you want your angles to be in radians, make sure your calculator is in "Radian Mode". If you want your angles to be in degrees, your calculator must be in "Degree Mode."

This calculation will result in approximately

59.32or^{o}radians.1.04

Example 2:

Using a calculator, find

in degrees and radians rounded to two decimal places.cos^{ }^{ -1}(0.87)You access

by first pressing the "2nd" or "Shift" key on your calculator and then pressing the "cos" key.cos^{ }^{ -1}This calculation results in approximately

29.54or^{o}radians.0.52

Example 3:

Using a calculator, find

in degrees and radians rounded to two decimal places.tan^{ }^{ -1}(0.59)You access

by first pressing the "2nd" or "Shift" key on your calculator and then pressing the "tan" key.tan^{ -1}This calculation results in approximately

30.54or^{o}radians0.53

Example 4:

Compare some trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarcsin(0.5)gives us back an angle of30.^{o}

Example 5:

Compare some trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarccos(0.5)gives us back an angle of60.^{o}

Example 6:

Compare some trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarctan(1)gives us back an angle of45.^{o}

Example 7:

Let's compare some more trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarcsin(0.5)DOES NOT gives us back an angle of210.^{o}

WHY?Due to the range restrictions for the inverse sine function to

90^{o}y, the calculator gives us the angle from the restricted range. That's why the90^{o}isarcsin(0.5)and not30^{o}.210^{o}

Example 8:

Compare some trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarccos(0.5)DOES NOT gives us back an angle of240.^{o}

WHY?Due to the range restrictions for the inverse cosine function to

0^{o}y, the calculator gives us the angle from the restricted range. That's why the180^{o}isarccos(0.5)and not120^{o}.240^{o}

Example 9:

Compare some trigonometric functions with their inverses. KEEP YOUR CALCULATOR IN DEGREE MODE!

Given

let

Then

Given

let

Then

Please note thatarctan(1)DOES NOT gives us back an angle of135.^{o}

WHY?Due to the range restrictions for the inverse tangent function to

<90^{o}<y, the calculator gives us the angle from the restricted range. That's why the90^{o}isarctan(1)and not45^{o}.135^{o}