Trigonometry — practice questions, page 3
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The expression sin⁸θ − cos⁸θ is equal to:If 2sinθ + 3cosθ = 2, then 3sinθ − 2cosθ equals:If secθ = x + 1/(4x), then secθ + tanθ equals:If tanθ + secθ = √3 and 0° < θ < 90°, then θ equals:If tan²θ = 1 − e², then secθ + tan³θ·cosecθ equals:For sinθ ≠ cosθ, the expression (cos³θ − sin³θ)/(cosθ − sinθ) simplifies to:The sides of a right triangle are in the ratio 3 : 4 : 5. The sine of its smallest angle is:The value of (1 − tan15°)/(1 + tan15°) is:The product (secθ + tanθ)(1 − sinθ) simplifies to:Standing at the edge of one bank of a river, a surveyor sees the top of a tree growing at the edge…If sinθ + cosθ = m and sinθ·cosθ = n, then m² equals:For every acute angle θ, which pair of expressions is always equal?A vertical tower 10 m high carries a flagstaff standing upright at its top. From a point on level…The expression (sin70° + sin10°)/(cos70° + cos10°) equals:In an integral involving √(9 − x²) a student substitutes x = 3sinθ with θ acute. The radical then…If tanθ + cotθ = 5, then tan²θ + cot²θ equals:A vertical stick 6 m long casts a shadow 4 m long on level ground. At the same moment a nearby…Which one of the following statements is TRUE?The expression (1 − cos²θ)(1 + cot²θ) simplifies to:From a point exactly midway between the feet of two vertical towers standing on level ground, the…Under the substitution x = 2tanθ with θ acute, the expression √(4 + x²) becomes:The greatest value of 12sinθ − 9sin²θ as θ varies is:A tree is snapped by the wind but the broken part stays attached and leans over so that its tip…Given that tan15° = 2 − √3, the value of tan75° is:The expression cos⁴θ − sin⁴θ + 1 is equal to:
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