C

9000046505

Level: 
C
Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation. \[ \sin x = 1 +\cos x \]
\(\sin ^{2}x = 1 + 2\cos x +\cos ^{2}x\)
\(\sin ^{2}x = 1 +\cos ^{2}x\)
substitution \( 1 +\cos x = z\)
\(\sin x -\cos x = z\)

9000046507

Level: 
C
Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation. \[ \sqrt{3}\cos x = 1 -\sin x \]
\(3\cos ^{2}x = (1 -\sin x)^{2}\)
\(3\cos ^{2}x = 1 -\sin ^{2}x\)
substitution \( 1 -\sin x = z\)
substitution \( \cos x = z\)

9000046508

Level: 
C
Identify the optimal first step convenient to solve the following trigonometric equation. Do not consider the step which is possible but does not help to solve the equation. \[ \sqrt{3}\sin x = 2 -\cos x \]
\(3\sin ^{2}x = 4 - 4\cos x +\cos ^{2}x\)
substitution \( 2 -\cos x = z\)
\(3\sin ^{2}x = 4 -\cos ^{2}x\)
\(3\sin ^{2}x = 1 - 2\cos x +\cos ^{2}x\)

9000036107

Level: 
C
There are three information panels \(A\), \(B\) and \(C\) in the park. The direct distance between \(B\) and \(C\) is \(150\, \mathrm{m}\). The visual angle of this distance from the panel \(A\) is \(55^{\circ }\). The visual angle of the distance \(AC\) from the panel \(B\) is \(39^{\circ }\). Find the direct distance between the panels \(A\) and \(B\) and round your answer to nearest meters.
\(183\, \mathrm{m}\)
\(147\, \mathrm{m}\)
\(195\, \mathrm{m}\)
\(218\, \mathrm{m}\)

9000036108

Level: 
C
The center of a spherical balloon is at a height of \(500\, \mathrm{m}\) height. The visual angle of the balloon is \(1^{\circ }30'\). The elevation angle of the center of the balloon is \(42^{\circ }50'\). Find the diameter of the balloon in meters and round to nearest one decimal.
\(19.3\, \mathrm{m}\)
\(18.2\, \mathrm{m}\)
\(18.9\, \mathrm{m}\)
\(19.5\, \mathrm{m}\)

9000036109

Level: 
C
The point \(A\) is located \(20\, \mathrm{cm}\) from a mirror and the point \(B\) is located \(50\, \mathrm{cm}\) from the same mirror. The direct distance between \(A\) and \(B\) (the length of the segment \(AB\)) is \(70\, \mathrm{cm}\). Find the angle of incidence of the ray through the point \(A\) which is reflected to the point \(B\) and round your answer to nearest degrees. (The angle of incidence is the angle between the incident ray and the normal to the mirror.)
\(42^{\circ }\)
\(37^{\circ }\)
\(38^{\circ }\)
\(48^{\circ }\)