What is the angle that maximizes R?

In summary, the conversation discusses solving for the angle that maximizes the distance traveled by an object launched up an inclined plane, given its initial velocity and angle of launch. The equation for the distance traveled is R = V^2(sqrt 2)/ 32 (2sinthetacostheta - 2cos^2theta), and the equation for finding the angle that maximizes R is 2sinthetacostheta + 1 - 2sin^2theta = 0. The conversation also mentions using the identities sin(2x) = 2sinxcosx and cos(2x) = 2cos^x - sin^2x, and discusses how to solve for an equation
  • #1
TN17
47
0

Homework Statement



Sorry for the long intro:

An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz.
If air resistance is ingored, the distance, R, traveled by the object up the inclined plane, is
R = V^2(sqrt 2)/ 32 (2sinthetacostheta - 2cos^2theta

Question
You are asked to find the angle that maximizes R by solving equation
2sinthetacostheta + 1 - 2sin^2theta = 0
Solve for theta.

Homework Equations


Not really any equations, just solving.

The Attempt at a Solution


I tried to continue with this, but I don't know what to do when there are two different identities.

Would I factor?
 
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  • #2
Do you know what sin(2x) and cos(2x) equal in terms of cosx and sinx?
 
  • #3
Mentallic said:
Do you know what sin(2x) and cos(2x) equal in terms of cosx and sinx?


Well, sin(2x) = 2sinxcosx
and cos(2x) = 2cos^x - sin^2x or 2cos^2x - 1 or 1- 2sin^2x
Is that what you mean?
 
  • #4
Yes, so do you see how you can change your equation in terms of sin(2x) and cos(2x)?

Now how would you go about solving something like sin(2x)=cos(2x)
You don't need to worry about the 2x for the moment, you can just think of it as any other variable angle.
 

1. What is a trig equation word problem?

A trig equation word problem is a type of math problem that involves using trigonometric functions and equations to solve real-world situations. These problems typically involve angles, distances, and measurements of objects and require the use of trigonometric identities and properties to find a solution.

2. How do I solve a trig equation word problem?

To solve a trig equation word problem, you first need to identify the given information and what you are trying to find. Then, you can use the appropriate trigonometric function and equation to set up an equation and solve for the unknown variable. It is important to understand the fundamental trigonometric principles and identities in order to successfully solve these types of problems.

3. What are some common trigonometric identities used in trig equation word problems?

Some common trigonometric identities used in trig equation word problems include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. These identities can help simplify equations and make them easier to solve.

4. Can you provide an example of a trig equation word problem?

Sure! An example of a trig equation word problem could be: "A 12-foot ladder is placed against a wall at a 60-degree angle. How far is the base of the ladder from the wall?" In this problem, you would use the trigonometric function tangent to set up an equation and solve for the distance.

5. How can I check my answer to a trig equation word problem?

You can check your answer to a trig equation word problem by plugging your solution back into the original equation and seeing if it satisfies the given conditions. You can also use a calculator or graphing software to visually confirm your answer.

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