Solving Trigonometric Equations: How to Find the Angle in @=33.40 Degrees

  • Thread starter Jac8897
  • Start date
In summary, to solve the equation sin@-.3cos@=.3 and find @=33.40 degrees, one should study the sine and cosine functions and use the fact that sin(pi) = 0 and cos(pi) = -1. By rewriting the left-hand side of the equation as sinθcosφ - cosθsinφ and setting .3 = sinφ/cosφ, one can easily solve for @ using a calculator.
  • #1
Jac8897
25
0
solving an equation??

Homework Statement


how to get from here
sin@-.3cos@=.3
to
@=33.40 degrees


Homework Equations





The Attempt at a Solution


I try every thing teacher said to put it in the calculator and find the where it intersects x-axis but I get @=30 degrees
 
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  • #2


this is pretty simple problem, I suggest you to study the sine and cosine functions well, and you will find that sin(pi) = 0 and cos(pi)=-1

Then sin(pi)-0.3*cos(pi)=0.3

0 + 0.3 = 0.3
 
  • #3
Hi Jac8897! :smile:

(have a theta: θ and a phi: φ :wink:)

The trick is to write the LHS in the form sinθcosφ - cosθsinφ …

in this case, put .3 = sinφ/cosφ :wink:
 

FAQ: Solving Trigonometric Equations: How to Find the Angle in @=33.40 Degrees

What is a trigonometric equation?

A trigonometric equation is an equation that involves one or more trigonometric functions, such as sine, cosine, or tangent, and an unknown angle. The goal is to solve for the unknown angle, typically in radians or degrees.

Why is it important to solve trigonometric equations?

Solving trigonometric equations allows us to find the measure of an unknown angle in a geometric problem. This is particularly useful in real-world applications, such as engineering, navigation, and physics.

What is the process for solving a trigonometric equation?

The process for solving a trigonometric equation involves using known trigonometric identities and properties to manipulate the equation and isolate the unknown angle. This often requires using inverse trigonometric functions, such as arcsine, arccosine, or arctangent.

How do you find the angle in @=33.40 degrees?

To find the angle in @=33.40 degrees, you can use the inverse tangent function. The inverse tangent of 33.40 degrees is approximately 0.583 radians or 33.40 degrees. This means that the angle in question is 33.40 degrees.

What are some common mistakes when solving trigonometric equations?

Some common mistakes when solving trigonometric equations include forgetting to use inverse trigonometric functions, not properly simplifying the equation, and not checking for extraneous solutions. It is important to double check your work and make sure your answer makes sense in the context of the problem.

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