If tan θ = 4/3, calculate sin\(^2\) θ - cos\(^2\) θ.
16/25
24/25
7/25
9/25
Correct answer is C
\(\tan \theta = \frac{opposite}{adjacent} = \frac{4}{3}\)
Hyp\(^2\) = 4\(^2\) + 3\(^2\)
Hyp = 5.
\(\sin \theta = \frac{4}{5}; \cos \theta = \frac{3}{5}\)
\(\sin^{2} \theta - \cos^{2} \theta = \frac{16}{25} - \frac{9}{25}\)
= \(\frac{7}{25}\)
4π cm2
32 π cm2
16 π cm2
8 π cm2
Correct answer is D
Diameter = 4\(\sqrt{3}\) cm<
radius = 2\(\sqrt{3}\) cm
Area of major sector = \(\frac{\theta}{360} \times \pi r^{2}\)
\(\theta = 360 - 120 = 240°\)
= \(\frac{240}{360} \times \pi \times 12\)
= \(8\pi cm^{2}\)
If x varies directly as √n and x = 9 when n = 9, find x when n = (17/9)
4
27
√3
√17
Correct answer is D
\(x \propto \sqrt{n}\)
\(x = k \sqrt{n}\)
\(9 = k \sqrt{9} \implies 9 = 3k\)
\(k = 3\)
\(x = 3 \sqrt{n}\)
When n = 17/9,
\(x = 3 \times \sqrt{\frac{17}{9}} = \sqrt{17}\)
The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is
11/3
10/3
5/2
3/2
Correct answer is D
The series is geometric with common ratio \(\frac{1}{3}\).
\(S_{\infty} = \frac{a}{1 - r}\)
= \(\frac{1}{1 - \frac{1}{3}} \)
= \(\frac{1}{\frac{2}{3}}\)
= \(\frac{3}{2}\)
59
19
67
38
Correct answer is A
\(p \ast q = pq + p + q\)
\(2 \ast (3 \ast 4) \)
\(3 \ast 4 = 12 + 3 + 4 = 19\)
\(2 \ast 19 = 38 + 2 + 19 = 59\)