Grade 11 Exam > Grade 11 Videos > Mathematics for Grade 11 > Proof: Trigonometric Ratios of Sum & Difference of Two Angle
Proof: Trigonometric Ratios of Sum & Difference of Two Angle Video Lecture | Mathematics for Grade 11
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FAQs on Proof: Trigonometric Ratios of Sum & Difference of Two Angle Video Lecture - Mathematics for Grade 11
| 1. What are the trigonometric ratios of the sum of two angles? |  |
Ans. The trigonometric ratios of the sum of two angles are given by:
- The sine of the sum of two angles is equal to the sum of the individual sines: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
- The cosine of the sum of two angles is equal to the product of the individual cosines minus the product of the individual sines: cos(A + B) = cos(A)cos(B) - sin(A)sin(B).
- The tangent of the sum of two angles is equal to the sum of the individual tangents divided by 1 minus the product of the individual tangents: tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)).
| 2. What are the trigonometric ratios of the difference of two angles? | |
Ans. The trigonometric ratios of the difference of two angles are given by:
- The sine of the difference of two angles is equal to the difference of the individual sines: sin(A - B) = sin(A)cos(B) - cos(A)sin(B).
- The cosine of the difference of two angles is equal to the product of the individual cosines plus the product of the individual sines: cos(A - B) = cos(A)cos(B) + sin(A)sin(B).
- The tangent of the difference of two angles is equal to the difference of the individual tangents divided by 1 plus the product of the individual tangents: tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B)).
| 3. How can the trigonometric ratios of the sum and difference of two angles be derived? | |
Ans. The trigonometric ratios of the sum and difference of two angles can be derived using trigonometric identities such as the sum and difference formulas. These formulas allow us to express the trigonometric functions of the sum and difference of two angles in terms of the trigonometric functions of the individual angles. By substituting the values of sine, cosine, and tangent for each angle, we can simplify and derive the formulas for the sum and difference of two angles.
| 4. What are some applications of the trigonometric ratios of the sum and difference of two angles? | |
Ans. The trigonometric ratios of the sum and difference of two angles have various applications in fields such as physics, engineering, and navigation. Some examples include:
- Analyzing the motion of objects in two dimensions.
- Solving problems involving waves and interference.
- Calculating the angles of inclination and elevation in surveying and construction.
- Modeling the behavior of alternating current circuits.
- Navigating using celestial bodies and triangulation methods.
| 5. Can the trigonometric ratios of the sum and difference of two angles be used to solve real-life problems? | |
Ans. Yes, the trigonometric ratios of the sum and difference of two angles can be used to solve real-life problems that involve angles and trigonometric functions. By applying these formulas, we can calculate unknown angles or distances, analyze the relationship between angles, and solve various geometric and physics-related problems. The key is to properly identify the given information, determine the appropriate trigonometric ratio to use, and apply the formulas accordingly.
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Dec 23, 2024 Last updated |
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