# Solving a Trigonometric Equation: v^2*sin(180-2theta2)/g

• DeltaForce
In summary, the conversation discussed how to simplify the equation v^2*sin(180-2theta2)/g by using trigonometric identities, specifically the sum and difference identities for sine and cosine. The next step would be to simplify the equation using these identities to show that both sides are equal.
DeltaForce
Homework Statement
Show that the range of the projectile is the same for two different projection angles --- a pair that add up to 90 degrees.
Relevant Equations
theta1 +theta2 = 90

v^2 * sin(2theta1)/g = v^2 *sin(2theta2)/g
theta1 = 90- theta2
I substituted that into v^2*sin(2theta1)/g
So I get
v^2*sin(180-2theta2)/g

Now I'm stuck. What do I do next?

You need to go back to the equation. You need to show that the 2 sides of the equation are indeed equal, using some trigonometric identities. You may find this list of identities helpful. https://bitly.com/trigiden

Ohh... ok. So it has something to do with the sum and difference identities. Thank you.

DeltaForce said:
What do I do next
You ought to know how to simplify sin(180-x), sin(90-x), sin(180+x), and likewise with cos.

Yeah. I got it with the trig identities.

## 1. What is a trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions, such as sine, cosine, and tangent. These equations are often used to solve for unknown angles or sides in a triangle.

## 2. What is the general process for solving a trigonometric equation?

The general process for solving a trigonometric equation is to isolate the trigonometric function on one side of the equation and use inverse trigonometric functions to solve for the unknown angle or side. This may involve using algebraic techniques or trigonometric identities.

## 3. What is the purpose of the "v^2" and "g" terms in this equation?

The "v^2" term represents the initial velocity of an object and the "g" term represents the acceleration due to gravity. These terms are included in the equation to solve for the angle at which an object will be launched in order to reach a certain height or distance.

## 4. How do you use the "180-2theta2" term in this equation?

The "180-2theta2" term represents the angle at which the object will be launched. This term is used in the equation to account for the fact that the object will be launched at an angle, rather than directly upward. It is important to use the correct angle in order to accurately solve the equation.

## 5. Can this equation be applied to real-world situations?

Yes, this equation can be applied to real-world situations, such as calculating the ideal angle for launching a projectile in order to reach a specific target or determining the angle at which a ramp should be built for a car to reach a certain height. It can also be used in physics and engineering applications to solve for various variables in projectile motion problems.

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