Question

sinx=-1/2 and tanx=1/√3 then x is equal to​

Answer 1

sinx=-1\2

x=sin inverse (-1/2)

since sin function is. negative on 3rd and 4th quedrent so the ans is

x=π+π/6 and 3π/2 +π\6=210°and 300°

for tanx=1/root 3

x=tan inverse 1/root3

x=π\6 and π+π/6=30°and 210°

so both equation satisfy at 210° and ans become 210°

Answer 2

Therefore, x is 7π/6 or, 210°

Given

• sinx=-1/2
• tanx=1/√3

To Find

Value of x

Solution

We know that

• All functions of tan and cot are positive in the first and third quadrants.
• All functions of sin and cosec are positive in the first and second quadrants.
• of cos and sec are positive in the first and fourth quadrants.

Now, tanx = 1/√3

x = tan⁻¹1/√3

Since tanx is positive, x lies either in first or third quadrant

Therefore,

x = π/6 or, π + π/6                               [1]

Now, sinx = -1/2

Since sinx is negative, x lies either in the third or fourth quadrant

Therefore,

x =  π + π/6 or, -π/6                             [2]          

From equations [1] and [2] we get

x = π + π/6

= 7π/6 or, 210°

Therefore, x is 7π/6 or, 210°

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