Math  /  Geometry

Questiona) Solve the trigonometric equation: 5sinϕ+3=05 \sin \phi+3=0 for values of ϕ\phi from 00^{\circ} to 360360^{\circ}. [9 marks] b) Use the diagram provided below to answer the following questions. i. Calculate the length of PR|P R|, correct to the nearest whole number. [4 marks] ii. show that PSR=90\angle \mathrm{PSR}=90^{\circ} [5 marks] c) Determine whether or not the ordered triple (8,6,9)(8,6,9) is a Pythagorean triple? [2 marks]

Studdy Solution
Calculate:
82+62=64+36=1008^2 + 6^2 = 64 + 36 = 100 92=819^2 = 81
Since 10081100 \neq 81, (8,6,9)(8, 6, 9) is not a Pythagorean triple.
The solutions are: a) ϕ1=180+θ\phi_1 = 180^\circ + \theta, ϕ2=360θ\phi_2 = 360^\circ - \theta b) i. PR7m|PR| \approx 7 \, \text{m} ii. PSR=90\angle PSR = 90^\circ c) (8,6,9)(8, 6, 9) is not a Pythagorean triple.

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