If r cosθ = 2√3 and r sinθ = 2, then find the value of r and θ when 0° < θ < 90°.
WBBSE
Class X
Mathematics
Trigonometric Ratio of Complementary Angle
02 Mark
2024
r cosθ = 2√3 —– (i)
r sinθ = 2 —– (ii)
Dividing (ii) by (i)
r sinθ ÷ r cosθ = 2 ÷ 2√3
⇒ tan θ = 1 ÷ √3
⇒ tan θ = tan 30°
∴ θ = 30°
Put θ in equation (i)
r cosθ = 2√3
⇒ r cos 30° = 2√3
⇒ r √3 ÷ 2 = 2√3
⇒ r = 4
∴ r = 4 and θ = 30°
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