Trigonometry: Determining the values of Trigonometric Ratios

Determining the values of Trigonometric Ratios

Example: Using the formula tan2= 2tan/(1-tan2), find the value of tan 60, given that tan 30=1/3.
Solution: Putting = 30 in the given formula gives
 tan 60
= 2 tan 30/(1- tan230)
= (2 x 1/3)/(1 - (1/3)2)
=  (2/3)/(2/3)
= 3
Hence, tan 60 = 3.
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Example: Using the formula, sin(A-B) = sinAcosB - cosAsinB, find the value of sin 15.
Solution: Let A = 45 and B = 30. So A - B = 15. Putting A = 45 and B = 30 in the given formula gives
 or sin(45 - 30) = sin 45 cos 30 - cos 45 sin 30 sin(45 - 30) = 1/2 x 3/2 - 1/2 x 1/2 = (3-1)/22 sin 15 = (3-1)/22

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