What is the general solution for sin(x)= 5/13 ,tan(x), pi/2 <= x<= pi ?

The general solution for sin(x)= 5/13 ,tan(x), pi/2 <= x<= pi is No Solution for x\in\mathbb{R}

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sin(x)= 5/13 ,tan(x), pi/2 <= x<= pi

sin (x) = \frac{5}{13}, tan (x), \frac{π}{2} \leq x \leq π

No Solution for x \in R

Solution steps

sin (x) = \frac{5}{13}, tan (x), \frac{π}{2} \leq x \leq π

Apply trig inverse properties

sin (x) = \frac{5}{13}

General solutions for

sin (x) = \frac{5}{13}

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

x = arcsin (\frac{5}{13}) + 2 πn, x = π - arcsin (\frac{5}{13}) + 2 πn

x = arcsin (\frac{5}{13}) + 2 πn, x = π - arcsin (\frac{5}{13}) + 2 πn

Solutions for the range

tan (x)

No Solution for x \in R

sin (x) + cos^{2} (x) = \frac{5}{4}

2 cos^{2} (θ) - 5 cos (θ) - 3 = 0

15 sin (x) + 6 cos (x) - 3 = 0

1 + cot^{2} (x) = 8

\frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )} = 2 csc^{2} (x)

What is the general solution for sin(x)= 5/13 ,tan(x), pi/2 <= x<= pi ?
The general solution for sin(x)= 5/13 ,tan(x), pi/2 <= x<= pi is No Solution for x\in\mathbb{R}