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1.7 Trigonometry

1.7 Trigonometry

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Question 177

The potential difference VVV, in millivolts, across a resistor in an alternating current circuit is modeled by the function V(t)=7cos⁡t−24sin⁡tV(t) = 7\cos t - 24\sin tV(t)=7cost−24sint, where t t\,t is the time in milliseconds since the circuit was closed.

a.

Express V(t)V(t)V(t) in the form Rcos⁡(t+α)R\cos(t + \alpha)Rcos(t+α), where R>0 R > 0\,R>0 and 0<α<π2\displaystyle 0 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of R R\,R and the value of α\alphaα, in radians, to 3 decimal places.

[3]
b.

The curve with equation y=cos⁡ty = \cos ty=cost is transformed onto the curve with equation y=V(t)y = V(t)y=V(t) by a sequence of two transformations.

Given that the first transformation is a stretch and the second is a translation:

(i) Describe fully the transformation that is a stretch. (ii) Describe fully the transformation that is a translation.

[2]
c.

The power efficiency G G\,G of a specific component is given by G(t)=210075+(V(t))2\displaystyle G(t) = \frac{2100}{75 + (V(t))^2}G(t)=75+(V(t))22100​. Find the range of GGG.

[4]
Markscheme

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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