Podcast
Questions and Answers
Simplify the expression: $\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$
Simplify the expression: $\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ}$
- sin 60
- cos 60
- sin 30
- tan 60 (correct)
Simplify the expression: $\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}$
Simplify the expression: $\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}$
- sin 45
- sin 30
- 1 (correct)
- tan 90
The equation sin 2A = 2 sin A is true when A is equal to:
The equation sin 2A = 2 sin A is true when A is equal to:
- 30
- 0 (correct)
- 45
- 60
If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$, where 0 < A + B 90 and A > B, find the values of A and B.
If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$, where 0 < A + B 90 and A > B, find the values of A and B.
Sin(A + B) = sin A + sin B
Sin(A + B) = sin A + sin B
The value of cos is always bounded between 0 and 1.
The value of cos is always bounded between 0 and 1.
Sin = cos for all values of .
Sin = cos for all values of .
Cot A is undefined when A = 0.
Cot A is undefined when A = 0.
Flashcards
What is the tangent of an angle?
What is the tangent of an angle?
The tangent of an angle is the ratio of the opposite side to the adjacent side.
What is the sine of an angle?
What is the sine of an angle?
The sine of an angle is the ratio of the opposite side to the hypotenuse.
What is the cosine of an angle?
What is the cosine of an angle?
The cosine of an angle is the ratio of the adjacent side to the hypotenuse.
What are trigonometric identities?
What are trigonometric identities?
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What is the double angle formula for sine?
What is the double angle formula for sine?
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What is the double angle formula for tangent?
What is the double angle formula for tangent?
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How do you find the values of sin, cos, and tan for specific angles like 30°, 45°, and 60°?
How do you find the values of sin, cos, and tan for specific angles like 30°, 45°, and 60°?
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What happens to the value of sine as the angle increases from 0° to 90°?
What happens to the value of sine as the angle increases from 0° to 90°?
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What happens to the value of cosine as the angle increases from 0° to 90°?
What happens to the value of cosine as the angle increases from 0° to 90°?
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What is the value of tan 90°?
What is the value of tan 90°?
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What are trigonometric functions?
What are trigonometric functions?
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What is the relationship between sine and cosine of complementary angles?
What is the relationship between sine and cosine of complementary angles?
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Is sin(A + B) equal to sin A + sin B?
Is sin(A + B) equal to sin A + sin B?
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When is cot A undefined?
When is cot A undefined?
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What is the Pythagorean identity?
What is the Pythagorean identity?
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How can trigonometric ratios be used to solve right triangles?
How can trigonometric ratios be used to solve right triangles?
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What is the relationship between tangent, sine, and cosine?
What is the relationship between tangent, sine, and cosine?
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What is the value of tan 45°?
What is the value of tan 45°?
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What is the value of sin 30°?
What is the value of sin 30°?
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Study Notes
Trigonometric Identities and Equations
-
Question 1: Solve for the value of 2 tan 30° / (1 + tan² 30°)
- Options: A) sin 60°, B) cos 60°, C) tan 60°, D) sin 30°
- Correct answer: A) sin 60°
-
Question 2: Solve for the value of 1 - tan² 45° / 1 + tan² 45°
- Options: A) tan 90°, B) 1, C) sin 45°, D) 0
- Correct answer: B) 1
-
Question 3: Solve for the value of A if sin 2A = 2 sin A
- Options: A) 0°, B) 30°, C) 45°, D) 60°
- Correct answer: C) 45°
-
Question 4: Evaluate 2 tan 30° / (1 - tan² 30°)
- Options: A) cos 60°, B) sin 60°, C) tan 60°, D) sin 30°
- Correct answer: B) sin 60°
-
Question 5: If tan (A + B) = √3 and tan (A - B) = 1/√3, where 0° < A + B ≤ 90° and A > B, find the values of A and B
- This requires additional information to find the values of A and B
Trigonometric Identities
- Identities: Trigonometric identities involving sin(A + B), sin(A - B), tan(A + B), tan(A - B), and relationships between sin 2A and sin A are analyzed and assessed for truthfulness in various conditions.
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