Question

Question 10 Find sin(x/2), cos(x/2) and tan(x/2) for sin x = 1/4, x in quadrant II

Class X1 - Maths -Trigonometric Functions Page 82

Answer 1

sinx = 1/4 where x lies on 2nd quadrant .
means 90° < x < 180°
so, 45° < (x/2) < 90° hence, (x/2) lies on 1st quadrant .

sinx = 1/4 = p/h
b = √(4²-1²) = √(16-1) = √15
cosx = -√15/4 [ because x lies on 2nd quadrant]

now,
cosx = 2cos²(x/2) -1 [by formula]
-√15/4 = 2cos²(x/2)-1
-√15/4 + 1 = 2cos²(x/2)
(4 - √15)/4 = 2cos²(x/2)
cos(x/2) = √(8-2√15)/4

again,
sin²(x/2) = 1 - cos²(x/2)
= 1 - (8- 2√15)/16
= ( 8 + 2√15)/16

sin(x/2) = √(8+2√15)/4

tan(x/2) = sin(x/2)/cos(x/2)
= √(8 + 2√15)/√(8-2√15)

Answer 2

Step-by-step explanation:

sinx=-4÷3 ,x in 2nd quandrat