Podcast
Questions and Answers
If $ an heta = rac{12}{5}$, what expression can be proved equal to $ rac{7}{17}$?
If $ an heta = rac{12}{5}$, what expression can be proved equal to $ rac{7}{17}$?
If $ an heta = rac{1}{2}$, what is the value of $ rac{ an heta + an^2 heta}{ an heta + 1}$?
If $ an heta = rac{1}{2}$, what is the value of $ rac{ an heta + an^2 heta}{ an heta + 1}$?
If $ rac{3 an A - 4 an^2 A}{ an A}$ = 0, what can be concluded about $ an A$?
If $ rac{3 an A - 4 an^2 A}{ an A}$ = 0, what can be concluded about $ an A$?
Given $ an heta = rac{20}{21}$, how can $ rac{1+ an heta}{1- an heta}$ be simplified?
Given $ an heta = rac{20}{21}$, how can $ rac{1+ an heta}{1- an heta}$ be simplified?
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If $ an heta = rac{1}{ an heta}$, which of the following statements is true?
If $ an heta = rac{1}{ an heta}$, which of the following statements is true?
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If $ an heta = rac{1}{ an heta}$, what is $ an^2 heta$ equal to?
If $ an heta = rac{1}{ an heta}$, what is $ an^2 heta$ equal to?
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If $ an A = rac{3}{4}$, what expression evaluates to $ rac{3}{7}$?
If $ an A = rac{3}{4}$, what expression evaluates to $ rac{3}{7}$?
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What is true if $ an A = rac{1}{ an A}$?
What is true if $ an A = rac{1}{ an A}$?
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Flashcards
Trigonometric Ratio
Trigonometric Ratio
A ratio between two sides of a right-angled triangle, based on an acute angle.
Tan θ = 12/5
Tan θ = 12/5
Indicates the ratio of the side opposite to angle θ to the side adjacent to angle θ is 12/5 in a right-angled triangle.
Sin θ = 12/13
Sin θ = 12/13
The ratio of the side opposite to angle θ to the hypotenuse in a right-angled triangle is 12/13.
Tan θ = 1/2
Tan θ = 1/2
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Sin α = 1/2
Sin α = 1/2
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Cot θ = 8/15
Cot θ = 8/15
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Sec θ = 17/8
Sec θ = 17/8
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Tan θ = 20/21
Tan θ = 20/21
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Study Notes
Trigonometric Ratios
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If tan θ = a/b, then (sin θ - b cos θ) / (sin θ + b cos θ) = (a² - b²) / (a² + b²)
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If sin θ = 13/12, evaluate (2 sin θ - 3 cos θ) / (4 sin θ - 9 cos θ)
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If tan θ = 1/2, evaluate (cos θ + sin θ) / (sin θ + 1 + cos θ)
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If sin α = 1/2, prove (3 cos α - 4 cos² α) = 0
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If 3 cot θ = 2, prove (4 sin θ - 3 cos θ) / (2 sin θ + 6 cos θ) = 1/3
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If sec θ = 17/8, prove 3 - 4 sin² θ = 3 - tan² θ / 4 cos² θ - 1
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If tan θ = 20/21, prove (1 - sin θ + cos θ) / (1 + sin θ + cos θ) = 3/7
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If tan θ = 1/√7, prove (cosec² θ + sec² θ) / (cosec² θ - sec² θ) = 4/3
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If sin θ = 3/4, prove cosec² θ - cot² θ / sec θ - 1 = √7/3
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If 3 tan A = 4, prove (i) (sec A - cosec A) / (sec A + cosec A) = 1/√7 and (ii) (1 - sin A) / (1 + cos A) = 1/2√2
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If cot θ = 15/8, evaluate (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ)
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In ΔABC, if ∠B = 90° and tan A = 1, prove 2 sin A cos A = 1
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In rectangle ABCD, diagonal AC = 17 cm, ∠BCA = θ, sin θ = 8/17. Find (i) area of ABCD, (ii) perimeter of ABCD
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If x = cosec A + cos A and y = cosec A - cos A, prove (x²/2) + (y²/2) / (x + y) = 1
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Description
Test your understanding of trigonometric ratios and identities with this quiz. It includes various proofs and evaluations based on fundamental trigonometric principles. Challenge yourself with problems involving sine, cosine, tangent, and cotangent.
