Everyone. In this problem, we are asked to find all of the solutions to the equation the sine of theta equals 12. But we want to express these solutions in degrees. So we're going to have to keep that in mind as we go about solving this. Now here we want to start by finding all of the solutions that are on our unit circle. So we want to find our angles for which the sine is equal to 12. Now coming over here to my unit circle, I know that the sine of π6 is 12, and then also over here in quadrant 2, that's the other quadrant for which my sine values are positive. I know that the sine of 5π6 will also be positive 12. So my solutions on my unit circle are theta equals π6 and theta equals 5π6. Now I'm going to stop here and go ahead and convert these into degrees. Now these are radian measures. So whenever we have radian measures, we can simply multiply them by 180 degrees over π in order to convert them to degrees. So let's go ahead and do that to both of these radian angle measures. So I want to multiply this by 180°/π and then multiply 5π6 also by 180°/π. Now for that π6 times 180 over π, those πs are, of course, going to cancel, leaving me with 180 divided by 6. Now this gives me a value of 30 degrees. Now for 5π6, again, those πs are going to cancel, and I'm going to be left with 5 times 180 over 6, which gives me an angle measure of 150 degrees. Now, you might also just have these values memorized from looking at your unit circle, but remember that you can always calculate them by simply multiplying your radian angle measure by 180 over π. Now from here, we have our angle measures in degrees. But remember, we want to find all of the solutions here. So we want to add multiple rotations to these. Now typically, we add 2πn, but 2πn is in radians. So instead of 2π, I want to express a full rotation in degrees. So instead of 2πn, I am instead going to have 360 degrees times n to each of these to represent multiple rotations but in degrees. So here, my final solutions are 30 degrees plus 360n and 150 degrees plus 360n. Thanks for watching, and I'll see you in the next one.
Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles39m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
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- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
11. Inverse Trigonometric Functions and Basic Trig Equations
Linear Trigonometric Equations
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