Finding the Exact Value of sin[2arcsin(3/5)] with Inverse Trig Functions

In summary, to find the exact value of the expression sin[2arcsin(3/5)], you can first let u = arcsin(3/5) and then use the identity sin2x = 2sinxcosx. Drawing a right triangle and labeling the sides and hypotenuse can be helpful in solving the expression. The final answer is 24/25.
  • #1
page13
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0

Homework Statement


Find the exact value of the expression:


Homework Equations


sin[2arcsin(3/5)]


The Attempt at a Solution


I know you're supposed to use sin2x=2sinxcosx somehow but not sure how to start.
 
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  • #2
page13 said:

Homework Statement


Find the exact value of the expression:


Homework Equations


sin[2arcsin(3/5)]


The Attempt at a Solution


I know you're supposed to use sin2x=2sinxcosx somehow but not sure how to start.

Start by letting u = arcsin(3/5). Then your expression is sin(2u) = ?

It will be helpful to draw a right triangle where u is one of the acute angles. Label the sides and hypotenuse so that sin(u) = 3/5.
 
  • #3
Ah, OK! 24/25 correct?
 

What is an inverse trig function?

An inverse trig function is a mathematical function that reverses the action of a trigonometric function. It calculates the angle measure when given the ratio of sides in a right triangle.

What are the most common inverse trig functions?

The most common inverse trig functions are arcsine (sin-1), arccosine (cos-1), and arctangent (tan-1).

How do you solve for an inverse trig function?

To solve for an inverse trig function, you must isolate the trigonometric function on one side of the equation and then apply the inverse trig function to both sides.

What is the domain and range of an inverse trig function?

The domain of an inverse trig function is the set of all possible input values, which is typically between -1 and 1. The range is the set of all possible output values, which is usually between -π/2 and π/2 for arcsine and arccosine, and between -π/2 and π/2 for arctangent.

How are inverse trig functions used in real life?

Inverse trig functions are commonly used in engineering, physics, and navigation to calculate angles and distances. They are also used in fields such as computer graphics and animation to create realistic 3D models.

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