Question

cos(0)=√2/2, and 3π/2<0<2π, evaluate sin(0) and tan(0). Sin(0)?

Answer 1

Answer:

Option (2)

Step-by-step explanation:

In this question we have to find the values of Sinθ and tanθ where $\frac{3\pi}{2}<x<2\pi$.

Cosθ = $\frac{\sqrt{2}}{2}$ ⇒ θ = $\frac{7\pi }{4}$

[Since $\text{Cos}\frac{7\pi }{4}=\text{Cos}(2\pi-\frac{\pi}{4})$

                     $=\text{Cos}\frac{\pi }{4}$

                     $=\frac{\sqrt{2} }{2}$ ]

Since Cosine of any angle between $\frac{3\pi}{2}$ and 2π is positive and Sine is negative in nature,

$\text{Sin}\frac{7\pi }{4}$ = $-\frac{\sqrt{2}}{2}$

Since, tanθ = $\frac{\text{Sin}\theta}{\text{Cos}\theta}$

tanθ = $\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} }$

       = $-\frac{\sqrt{2}}{2}\times \frac{2}{\sqrt{2}}$

       = -1

Therefore, Option (2) will be the answer.