If sin θ + cos θ = 9 5 and sin θ cos θ = 4 5 , then what is the value of sin θ and cos θ ?

Given, sin θ + cos θ = 9 5 ⇒ sin θ = 9 5 - cos θ Also, sin θ cos θ = 4 5 Now, consider sin θ = x and cos θ = y Thus, we get 9 5 - y × y = 4 5 ⇒ 9 y 5 - y 2 = 4 5 ⇒ 9 y - 5 y 2 5 = 4 5 ⇒ 5 y 2 - 9 y + 4 = 0 ⇒ 5 y 2 - 5 + 4 y + 4 = 0 [Splitting the middle term] ⇒ 5 y 2 - 5 y - 4 y + 4 = 0 ⇒ 5 y y - 1 - 4 y - 1 = 0 ⇒ y - 1 5 y - 4 = 0 So, When y - 1 = 0 ⇒ y = 1 , then x = 4 5 When 5 y - 4 = 0 ⇒ y = 4 5 , then x = 1 Hence, we get When cos θ = 1 , sin θ = 4 5 When cos θ = 4 5 , sin θ = 1

The sum of two angles is 11 12 π and difference is 75 ° , find θ the angles in circular measure.

Given, Sum of two angles = 11 12 π = 11 × 180 ° 12 = 165 ° Difference of the angles = 75 ° Let the angles be x ° and y ° . So, x + y = 165 ° ⇒ x = 165 ° - y And, x - y = 75 ° ⇒ 165 ° - y - y = 75 ° ⇒ 2 y = 165 ° - 75 ° ⇒ y = 90 ° 2 = 45 ° So, x = 165 ° - 45 ° = 120 ° Thus, the value of a angle in circular measure is 180 ° = π c ∴ 120 ° = π 180 × 120 ° = 2 π 3 and 45 ° = π 180 ° × 45 ° = π 4 Hence, the measure of the angles in circular measure is 2 π 3 and π 4