First slide

Trignometry

Question

If A sin $θ$ = 3 and A cos $θ$ = 4,then select correct alternatives.
(i) A = 5 (ii) A = 7
(iii) $θ$ = 37° (iv) $θ$ = 53°

Moderate

A

(i, ii}
B

(ii, iv)
C

(i, iii)
D

(ii, iii)

Solution

A sin $θ$ = 3 and A cos $θ$ = 4
$\Rightarrow A^{2} (\sin^{2} θ + \cos^{2} θ) = 3^{2} + 4^{2}$
$A^{2} = 25 \Rightarrow A = 5$
$Also tanθ = \frac{3}{4} \Rightarrow θ = 37 °$

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