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}$?
- $ rac{ rac{ an heta - 1}{ an heta + 1}}{1}$
- $ rac{ rac{ an heta - rac{5}{12}}{1 + rac{12}{5}}}{1}$
- $ rac{ rac{ an heta + an rac{5}{12}}{ an heta - an rac{5}{12}}}{1}$
- $ rac{ an heta - rac{ an^2 heta}{1+ an^2 heta}}{1 + an heta}$ (correct)
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}$?
- $ rac{1/2 + 1/4}{3/4}$ (correct)
- $ rac{3/2}{3/2}$
- $ rac{1/2 + 1/4}{1}$
- $ rac{2/3}{1/3}$
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$?
- $ an A = 0$
- $ an A = 1$ or $ an A = rac{4}{3}$ (correct)
- $ an A = rac{4}{3}$
- $ an A = 1$
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?
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?
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?
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}$?
What is true if $ an A = rac{1}{ an A}$?
What is true if $ an A = rac{1}{ an A}$?
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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