# Question 25: Trigonometric equations. (Late Middle Palaeolithic).

QUESTION 25. TRIGONOMETRIC EQUATIONS (Late Middle Palaeolithic). θ = s/60 × 2π 8sin^2(θ) + 2sin(θ) – 1 = 0 2cos^2(θ) + √3cos(θ) = 0 a. Solve for θ and s. (Note: there are several possible θ values, find the specific angle that corresponds to both sine and cosine). 8sin^2(θ) + 4sin(θ) – 2sin(θ) – 1 = 0 4sin(θ)(2sin(θ) […]

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# Question 24: Trigonometric equations. (Lower Palaeolithic).

QUESTION 24. TRIGONOMETRIC EQUATIONS (Lower Palaeolithic). θ = s/60 × 2π 3sin^3(θ) + 2 = 13/8 2cos^2(θ) – √3cos(θ) = 0 a. Solve for θ and s. sin^3(θ) + 2/3 = 13/24 sin^3(θ) = 13/24 – 2/3 = -1/8 sin(θ) = ³√(-1/8) = -1/2 sin^-1(-1/2) =  θ – 2π = -π/6 θ = 2π + sin^-1(-1/2) = 11π/6 cos(θ)(2cos(θ) […]

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# Question 23: Trigonometry without equations (Upper Palaeolithic).

QUESTION 23. TRIGONOMETRY WITHOUT EQUATIONS (Upper Palaeolithic). θ = s/60 × 2π y = sin(θ) = -0.30901699437494 x = cos(θ) = 0.95105651629515 a. Solve for θ and s. sin^-1(y) = θ – 2π = -π/10 θ = 2π + sin^-1(y) = 19π/10 cos^-1(x) = 2π – θ = π/10 θ = 2π – cos^-1(x) = 19π/10 19π/10 = s/60 […]

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# Question 22: Trigonometric equations.

QUESTION 22. TRIGONOMETRIC EQUATIONS. θ = s/60 × 2π 3sin^3(θ)/4 = -3/32 6cos^2(θ)/12 = 3/8 a. Solve for θ and s. 3sin^3(θ) = -3/8 sin^3(θ) = -1/8 sin(θ) = ³√(-1/8) = -1/2 sin^-1(-1/2) =  θ – 2π = -π/6 θ = 2π + sin^-1(-1/2) = 11π/6 6cos^2(θ) = 9/2 cos^2(θ) = 3/4 cos(θ) = √(3/4) = √3/2 cos^-1(√3/2) = 2π […]

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# Question 21: Trigonometric equations.

QUESTION 21. TRIGONOMETRY AND RADIANS When creating your own trigonometry and radians questions know that if we are being lazy and starting from an angle of M/(73/6) and we want particularly pretty maths or simple fractions then θ needs 2 decimal places. Any less and there are 0 seconds, anymore and the seconds are not […]

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# Question 20: Trigonometric equations.

QUESTION 20. TRIGONOMETRY AND RADIANS When creating your own trigonometry and radians questions know that if we are being lazy and starting from an angle of M/(73/6) and we want particularly pretty maths or simple fractions then θ needs 2 decimal places. Any less and there are 0 seconds, anymore and the seconds are not […]

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# Question 19: Creating your own questions.

QUESTION 19. TRIGONOMETRY AND RADIANS When creating your own trigonometry and radians questions know that if we are being lazy and starting from an angle of M/(73/6) and we want particularly pretty maths or simple fractions then θ needs 2 decimal places. Any less and there are 0 seconds, anymore and the seconds are not […]