Problems
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130 problems
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1
Double-Angle Tangent in Quadrant II If sin β‘ ΞΈ = 3 5 and ΞΈ lies in Quadrant II, what is tan β‘ ( 2 ΞΈ ) ?
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Hard2Count Solutions of a Trig Equation For 0 β€ x < 2 Ο , how many solutions satisfy 2 cos β‘ 2 x β 3 sin β‘ x = 0 ?
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Hard3Law of Cosines Exact Side In β³ A B C , a = 8 , b = 11 , and β C = 60 β . What is the exact value of c ?
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Medium4Sine from Tangent in Quadrant III If tan β‘ ΞΈ = 5 12 and ΞΈ is in Quadrant III, what is sin β‘ ΞΈ ?
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Medium5Double-Angle Sine from Cosine If cos β‘ ΞΈ = β 12 13 and ΞΈ is in Quadrant II, what is sin β‘ ( 2 ΞΈ ) ?
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Hard6Cosine from a Quadrant IV Sine If sin β‘ ΞΈ = β 3 2 and ΞΈ is in Quadrant IV, what is cos β‘ ΞΈ ?
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Easy7Sum of Special-Angle Values What is sin β‘ 150 β + cos β‘ 60 β ?
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Easy8Tangent at a Coterminal Angle What is tan β‘ 225 β ?
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Easy9Recover Tangent from Secant If sec β‘ ΞΈ = β 5 4 and ΞΈ lies in Quadrant III, what is tan β‘ ΞΈ ?
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Medium10Simplify with the Pythagorean Identity For values where it is defined, simplify 1 β cos β‘ 2 x sin β‘ x .
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Medium11Simplify a Secant-Tangent Expression For values where it is defined, simplify sec β‘ 2 x β 1 tan β‘ x .
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Medium12Count Solutions of Cosine Double Angle For 0 β€ x < 2 Ο , how many solutions satisfy cos β‘ ( 2 x ) = 0 ?
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Hard13Solve a Double-Angle Sine Equation For 0 β€ x < 2 Ο , how many solutions satisfy 2 sin β‘ x cos β‘ x = 1 ?
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Hard14Count Tangent Equation Solutions For 0 β€ x < 2 Ο , how many solutions satisfy tan β‘ x = β 1 ?
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Medium15Law of Cosines with a 60-Degree Angle Two sides of a triangle are 7 and 9, and their included angle is 60 β . What is the exact length of the third side?
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