Question

If * sin A = 0.8 find i) cosA, ii) tanA, iii) 3sec²A-2tan²A+5

Answer 1

Answer:

i) 0.6

ii) 1.322

iii) 9.75

Step-by-step explanation:

$\sin^{2} (a) + \cos^{2}(a) = 1 \\ {0.8}^{2} + \cos^{2}(a) = 1 \\ \cos^{2}(a) = 1 - 0.64 = 0.36 \\ \cos(a) = 0.6$

$\sec(a) = \frac{1}{0.6} = \frac{5}{3} = 1.66$

$\sec^{2} (a) - 1 = \tan^{2} (a) \\ \tan(a) = \sqrt{ {1.66}^{2} - 1 } = \sqrt{2.75 - 1} \\ \tan(a) = 1.322$

$3 \sec {}^{2} (a) - 2 \tan {}^{2} (a) + 5 \\ = 3 \times {1.66}^{2} - 2 \times {1.322}^{2} + 5 \\ = 3 \times 2.75 - 2 \times 1.75 + 5 \\ = 8.25 - 3.5 + 5 = 9.75$