Problems

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130 problems
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1
Double-Angle Tangent in Quadrant II If sin ⁑ θ = 3 5 and θ lies in Quadrant II, what is tan ⁑ ( 2 θ ) ?
πŸ“
Hard
2
Count Solutions of a Trig Equation For 0 ≀ x < 2 Ο€ , how many solutions satisfy 2 cos ⁑ 2 x βˆ’ 3 sin ⁑ x = 0 ?
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Hard
3
Law of Cosines Exact Side In β–³ A B C , a = 8 , b = 11 , and ∠ C = 60 ∘ . What is the exact value of c ?
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Medium
4
Sine from Tangent in Quadrant III If tan ⁑ θ = 5 12 and θ is in Quadrant III, what is sin ⁑ θ ?
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Medium
5
Double-Angle Sine from Cosine If cos ⁑ ΞΈ = βˆ’ 12 13 and ΞΈ is in Quadrant II, what is sin ⁑ ( 2 ΞΈ ) ?
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Hard
6
Cosine from a Quadrant IV Sine If sin ⁑ ΞΈ = βˆ’ 3 2 and ΞΈ is in Quadrant IV, what is cos ⁑ ΞΈ ?
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Easy
7
Sum of Special-Angle Values What is sin ⁑ 150 ∘ + cos ⁑ 60 ∘ ?
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Easy
8
Tangent at a Coterminal Angle What is tan ⁑ 225 ∘ ?
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Easy
9
Recover Tangent from Secant If sec ⁑ ΞΈ = βˆ’ 5 4 and ΞΈ lies in Quadrant III, what is tan ⁑ ΞΈ ?
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Medium
10
Simplify with the Pythagorean Identity For values where it is defined, simplify 1 βˆ’ cos ⁑ 2 x sin ⁑ x .
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Medium
11
Simplify a Secant-Tangent Expression For values where it is defined, simplify sec ⁑ 2 x βˆ’ 1 tan ⁑ x .
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Medium
12
Count Solutions of Cosine Double Angle For 0 ≀ x < 2 Ο€ , how many solutions satisfy cos ⁑ ( 2 x ) = 0 ?
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Hard
13
Solve a Double-Angle Sine Equation For 0 ≀ x < 2 Ο€ , how many solutions satisfy 2 sin ⁑ x cos ⁑ x = 1 ?
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Hard
14
Count Tangent Equation Solutions For 0 ≀ x < 2 Ο€ , how many solutions satisfy tan ⁑ x = βˆ’ 1 ?
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Medium
15
Law of Cosines with a 60-Degree Angle Two sides of a triangle are 7 and 9, and their included angle is 60 ∘ . What is the exact length of the third side?
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Medium
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