Trigonometry — practice questions, page 11
Browse practice questions
QuestionEvaluate: tan5°·tan85° + tan15°·tan75° + tan25°·tan65° + tan35°·tan55° + tan45°·tan45° =QuestionIn triangle ABC the angle B is 60° and the sides satisfy b² = ac. The triangle must be:QuestionA vertical tower stands at the edge of the far bank of a straight river. From a point at water…QuestionFor an acute angle θ, three of these four expressions are equal to one another. Which is the odd…QuestionAs θ varies over all real values, the expression 7sinθ + 24cosθ is greatest at the angles where…QuestionWherever the tangent and the secant are both defined, the difference sec⁴θ − tan⁴θ is always equal…QuestionOn level ground the shadow of a vertical pole is exactly one third as long as the pole. The Sun's…QuestionAs θ runs over all real values, the point (x, y) with x = 5cosθ and y = 3sinθ always satisfies:QuestionA student argues: 'Since tan²θ = sec²θ − 1, we may write tanθ = √(sec²θ − 1) for every θ. At θ =…QuestionIn triangle ABC, ∠A = 45° and ∠B = 60°. The ratio a : b of the sides opposite them is:QuestionFor a given angle θ, the two numbers secθ + tanθ and secθ − tanθ are the roots of the quadratic x²…QuestionFrom the top of a building 30 m high, the angle of depression of the foot of a nearby vertical…QuestionAs θ takes every real value, the greatest value of cos(θ − 20°) + cos(θ + 40°) is:QuestionFor every angle θ, the value of sin²θ + sin²(90° − θ) + sin²(180° + θ) + sin²(270° − θ) is:QuestionAll the angles θ with 0° ≤ θ ≤ 180° for which sin2θ = cosθ are:QuestionIf sinθ + cosθ = a and sin³θ + cos³θ = b, then a and b always satisfy:QuestionThe three sides of a triangle measure 3 cm, 5 cm and 7 cm. Its area is:QuestionIn triangle ABC the angle C is a right angle and sinA = 3/5. The value of sinA·sinB + cosA·cosB is:QuestionFor every θ at which every factor is defined, (cosecθ − sinθ)(secθ − cosθ)(tanθ + cotθ) equals:QuestionA helicopter flies horizontally at a steady height of 600 m along a straight level road. At one…QuestionIn triangle ABC, right-angled at B, cos A = 5/13. What is tan A?QuestionIf 3 tan θ = 4, then the value of (3 sin θ + 2 cos θ)/(3 sin θ − 2 cos θ) isQuestionIf tan θ = 4/3 and θ is acute, find the value of sin θ.QuestionIf tan θ = 4/3 and θ is acute, find the value of sin θ + cos θ.QuestionIf sin θ = 3/5, then the value of tan θ is ?
← Previous · Page 11 of 12 · Next →