First slide

Trigonometric Identities

Question

If a = cos 2 and b = sin 7, then

Easy

A

a>0, b >0
B

ab <0
C

a>b
D

a <b

Solution

we have,
$\frac{π}{2} < 2^{c} < \frac{3 π}{4} and 2 π < 7^{c} < \frac{5 π}{2}$
$\Rightarrow 2^{c} is in second quadrant and 7^{c} is in first quadrant$
$\Rightarrow a = \cos 2^{c} < 0 and b = \sin 7^{c} > 0$
$\Rightarrow ab < 0$

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