###
**
Principal solution for sin x = ½
**

sin x = ½

Here sin is positive,

We know that

sin is positive in 1st and 2nd quadrant

Value in 1st Quadrant = 30°

Value in 2nd Quadrant = 180° – 30° = 150°

So, Principal solutions are

x = 30° = 30° × π/180 = π/6

x = 150° = 150° × π/180 = 5π/6

Thus, Principal solutions are

π/6 & 5π/6

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**
Principal solution for cos x = –1/√2
**

cos x = –1/√2

Here cos is negative,

We know that

cos is negative in 2nd and 3rd quadrant

Here, θ = 45°

Value in 2nd Quadrant = 180° – 45° = 135°

Value in 3rd Quadrant = 180° + 45° = 225°

So, Principal solutions are

x = 135° = 135° × π/180 = 3π/4

x = 225° = 225° × π/180 = 5π/4

Thus, Principal solutions are

3π/4 & 5π/4

###
**
Principal solution for tan x = –1
**

tan x = –1

Here tan is negative,

We know that

tan is negative in 2nd and 4th quadrant

Here, θ = 45°

Value in 2nd Quadrant = 180° – 45° = 135°

Value in 4th Quadrant = 360° – 45° = 315°

So, Principal solutions are

x = 135° = 135° × π/180 = 3π/4

x = 315° = 315° × π/180 = 7π/4

Thus, Principal solutions are

3π/4 & 7π/4