Check Your Solutions for Equations Homework

  • Thread starter Thread starter Enochfoul
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on verifying solutions for the trigonometric equations cos2θ = sin θ and sin 2θ - 1 = cos2θ. Participants emphasize the importance of checking results by substituting cos(2θ) with 2cos²(θ) - 1 for simplification. Graphing the equations from 0 to 360° is recommended to confirm the solutions visually. The consensus is that the provided solutions are correct and comprehensive.

PREREQUISITES
  • Understanding of trigonometric identities, specifically cos(2θ) and sin(2θ).
  • Familiarity with graphing functions within the range of 0 to 360°.
  • Basic skills in algebraic manipulation and substitution techniques.
  • Knowledge of the unit circle and its application in solving trigonometric equations.
NEXT STEPS
  • Learn about trigonometric identities, focusing on double angle formulas.
  • Explore graphing techniques for trigonometric functions to visualize solutions.
  • Study substitution methods in solving equations for enhanced problem-solving skills.
  • Investigate the implications of periodicity in trigonometric equations.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and anyone looking to enhance their problem-solving skills in trigonometric equations.

Enochfoul
Messages
54
Reaction score
2

Homework Statement


Hi Could somebody please check my working to see if I have solved the following equations properly?

Homework Equations


1) cos2θ = sin θ
2) sin 2θ - 1 = cos2θ


The Attempt at a Solution


Scanned working attached
 

Attachments

Physics news on Phys.org
Looked okay to me on quick look.

It is easy for you to check whether the results are correct! Just see if they work.

It is pretty obvious they are the only solutions. But if there were ever any doubt in a problem like this, you need only do a graph from 0 to 360°.
 
  • Like
Likes   Reactions: Enochfoul
Enochfoul said:

Homework Statement


Hi Could somebody please check my working to see if I have solved the following equations properly?

Homework Equations


1) cos2θ = sin θ
2) sin 2θ - 1 = cos2θ

The Attempt at a Solution


Scanned working attached
Check if all your results are solutions.
It would have been easier to substitute cos(2θ) with 2cos2(θ)-1.
 

Similar threads

Solving trigonometric equations as fractions of π
  • · Replies 5 ·
Replies
5
Views
3K
Trigonometric Equations Problems - Rather Confused
  • · Replies 1 ·
Replies
1
Views
2K
Need Help Proving Identities for Q1 and Q2 in Trigonometry
  • · Replies 4 ·
Replies
4
Views
2K
Help Understanding Trig Equation
  • · Replies 5 ·
Replies
5
Views
2K
Use power-reducing formulas to rewrite
  • · Replies 4 ·
Replies
4
Views
4K
Simplifying Sin[3θ] to Simplifying Trigonometric Expressions
  • · Replies 1 ·
Replies
1
Views
3K
Help with Trig Identity Simplification
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Solve cosθ = sin2θ/2 Using Trigonometric Identities?
  • · Replies 1 ·
Replies
1
Views
2K
Simplifying Trigonometric Expressions
  • · Replies 1 ·
Replies
1
Views
2K
Show that ##2 {\cos \theta} +(1- \tan \theta)^2≈ 3 - 2\theta##
  • · Replies 5 ·
Replies
5
Views
3K