An architect is designing a custom semicircular stained-glass window with center CCC and a diameter PCQPCQPCQ of length 16 m16\text{ m}16 m. To reinforce the structure, a horizontal metal support beam STSTST is placed parallel to the diameter PCQPCQPCQ, such that the endpoints SSS and TTT lie on the semicircular arc. The design specifies that the angle TCQTCQTCQ is 0.450.450.45 radians. A specific segment of tinted glass, labeled WWW, is bounded by the beam STSTST and the minor arc STSTST.
Show that, to 3 decimal places, the angle SCTSCTSCT is 2.2422.2422.242 radians.
Calculate the area of the tinted glass segment WWW, giving your answer in m2\text{m}^2m2 to one decimal place.
Determine the total perimeter of the tinted glass segment WWW, giving your answer in m\text{m}m to one decimal place.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
