# How do you calculate sin x = 0.29?

Nov 9, 2015

You will need to use a trigonometry calculator.

#### Explanation:

The sine function is positive in the first and second quadrants, so we can conclude that sin x will lie between $0 \mathmr{and} 180$ degrees. We also know that sine increases to 1 (at ${90}^{o}$), then decreases to 0 at $180$.

So, there will be two solutions to this problem. One will occur between $0 \mathmr{and} 90$ and the other between $90 \mathmr{and} 180$.

Using a Trig calculator:

$\arcsin \left(0.29\right) \approx {16.858}^{o}$

The other value, due to symmetry, will equal:

${180}^{o} - {16.858}^{o} \approx {163.142}^{o}$

The graph below shows how the line $y = 0.29$ intersects the sine graph at the two points $x = {16.86}^{o} \mathmr{and} {163.14}^{o}$

Hope that helped