Trigonometry — practice questions, page 2
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For acute θ with 13 sin θ = 5, find (5 sin θ − 2 cos θ)/tan θ.Simplify sin θ/(1 + cos θ) + (1 + cos θ)/sin θ.tan θ/(1 − cot θ) + cot θ/(1 − tan θ) simplifies to(sin θ − cosec θ)(cos θ − sec θ) is equal toFind the value of sin⁶θ + cos⁶θ + 3 sin²θ cos²θ.If sin θ + sin²θ = 1, find cos¹²θ + 3cos¹⁰θ + 3cos⁸θ + cos⁶θ + 2.For acute θ, cosec θ + cot θ = 5. Find cos θ.For acute θ with sin θ + cos θ = √2, find tan θ + cot θ.a cos θ + b sin θ = 4 and a sin θ − b cos θ = 3. Find a² + b².What does (sec θ − cos θ)(cosec θ − sin θ)(tan θ + cot θ) equal?For acute θ, sec θ − tan θ = 1/4. Find sin θ.θ is acute and 3 sin θ + 4 cos θ = 5. Find tan θ.2 cos²θ − 3 cos θ + 1 = 0 and 0° < θ < 90°. Find θ.θ is acute and 4 sin²θ − 3 = 0. Find cos 2θ.sin(θ + 36°) = cos θ, where θ and θ + 36° are acute. Find θ.2 sin²θ + 3 sin θ − 2 = 0 and θ is acute. Find θ.sec θ + tan θ = √3 and 0° < θ < 90°. Find θ.Find the least value of 16 sec²θ + 9 cos²θ.By how much does the greatest value of 5 cos θ + 12 sin θ + 7 exceed its least value?What is the least value of cos²θ − 6 cos θ + 12?Find the value of cos 20° cos 40° cos 80°.A + B = 45°, with A and B positive. Find (1 + tan A)(1 + tan B).Evaluate sin 25°/cos 65° + tan 20° tan 70°.Find (sin 1° · sin 2° · sin 3° ⋯ sin 89°) ÷ (cos 1° · cos 2° · cos 3° ⋯ cos 89°).Find cos²5° + cos²10° + cos²15° + … + cos²85°.
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