What is the general solution for sin(θ)= 3/5 ,cos(2θ) ?

The general solution for sin(θ)= 3/5 ,cos(2θ) is No Solution for θ\in\mathbb{R}

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sin(θ)= 3/5 ,cos(2θ)

sin (θ) = \frac{3}{5}, cos (2 θ)

No Solution for θ \in R

Solution steps

sin (θ) = \frac{3}{5}, cos (2 θ)

Apply trig inverse properties

sin (θ) = \frac{3}{5}

General solutions for

sin (θ) = \frac{3}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{3}{5}) + 2 πn, θ = π - arcsin (\frac{3}{5}) + 2 πn

θ = arcsin (\frac{3}{5}) + 2 πn, θ = π - arcsin (\frac{3}{5}) + 2 πn

Solutions for the range

cos (2 θ)

No Solution for θ \in R

1 1^{2} = 6^{2} + 7^{2} - 2 \cdot 6 \cdot 7 \cdot cos (x)

2 cos^{2} (x) + cos (x) = 1, 0 \leq x \leq 2 π

sin (\frac{θ}{2}) = \frac{7.83}{2 ( 4.35 )}

- 4 sin (c) - 2 = sin (c) + 1

cot^{2} (x) + 1 = 2

What is the general solution for sin(θ)= 3/5 ,cos(2θ) ?
The general solution for sin(θ)= 3/5 ,cos(2θ) is No Solution for θ\in\mathbb{R}