How Do You Isolate sin a in a Quadratic Trigonometric Equation?

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SUMMARY

The discussion focuses on isolating sin a in the quadratic trigonometric equation 6sin² a - 11sin a + 4 = 0, with a domain of -360 to 360 degrees. Participants emphasize the need to replace sin a with a variable, such as y, transforming the equation into a standard quadratic form: 6y² - 11y + 4 = 0. This approach simplifies the problem, allowing for the application of the quadratic formula to find values for y, which can then be used to determine the corresponding angles for sin a.

PREREQUISITES
  • Understanding of quadratic equations and the quadratic formula
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Ability to manipulate algebraic expressions
  • Familiarity with angle measurement in degrees
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  • Practice solving quadratic equations using the quadratic formula
  • Study the properties of trigonometric functions and their inverses
  • Explore the unit circle to understand angle solutions for sine
  • Learn about transformations of trigonometric equations
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Students preparing for exams in trigonometry, mathematics educators, and anyone looking to deepen their understanding of solving quadratic trigonometric equations.

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So, I know how to solve them in general, but this one in particular, what do you do when the sin or cos etc is squared?

6sin^2 a - 11sin a + 4 = 0 , domain is from -360 until 360 degrees

we learned that, you need to isolate sin a, and then find the possible angles. I just need to know how to isolate sin a.

so i thought maybe this...

6 (sin a + sin a) - 11sin a = -4

but i don't know from here on...
please help! exam is coming up!
 
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ditto_299 said:
So, I know how to solve them in general, but this one in particular, what do you do when the sin or cos etc is squared?

6sin^2 a - 11sin a + 4 = 0 , domain is from -360 until 360 degrees

we learned that, you need to isolate sin a, and then find the possible angles. I just need to know how to isolate sin a.

so i thought maybe this...

6 (sin a + sin a) - 11sin a = -4
What? sin^2 a is (sin a)(sin a) NOT "sin a+ sin a"?

but i don't know from here on...
please help! exam is coming up!
Perhaps it would be simpler to replace sin a by y:
6y^2- 11y+ 4= 0. Can you solve that quadratic equation? After finding solutions, that is, specific values for y, you can solve sin a= y.
 

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