Given that the measure of arc ED is , what is the measure of angle EFD if angle EFD is an inscribed angle that intercepts arc ED?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In a right triangle, if = , what is the value of ?
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Verified step by step guidance1
Identify the given information: \( \sin(\theta) = \frac{3}{5} \). This means in a right triangle, the ratio of the length of the side opposite angle \( \theta \) to the hypotenuse is \( \frac{3}{5} \).
Recall the Pythagorean identity relating sine and cosine: \( \sin^2(\theta) + \cos^2(\theta) = 1 \). This identity holds for any angle \( \theta \).
Substitute the given sine value into the identity: \( \left(\frac{3}{5}\right)^2 + \cos^2(\theta) = 1 \).
Calculate \( \left(\frac{3}{5}\right)^2 = \frac{9}{25} \), so the equation becomes \( \frac{9}{25} + \cos^2(\theta) = 1 \).
Solve for \( \cos^2(\theta) \) by subtracting \( \frac{9}{25} \) from both sides: \( \cos^2(\theta) = 1 - \frac{9}{25} = \frac{16}{25} \). Then take the positive square root (since cosine is positive in the context of a right triangle's acute angle): \( \cos(\theta) = \frac{4}{5} \).
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