How to solve this trig!!!!

apaul322

11

i got 2theta + Pi/3 = Pi/6 and 5Pi/6 but i dont know how to get the other two values?

Reply 1

Shaanv

17

Original post by apaul322

i got 2theta + Pi/3 = Pi/6 and 5Pi/6 but i dont know how to get the other two values?

Cosec(x)=1/sin(x)

Rewrite ur equation in terms of sin, rearrange and solve.

Then use ur CAST diagram or a graph to find all the solutions in the range.

Remember theta ranges from -pi to pi. But the term inside ur brackets is 2theta+pi/3 so u have to adjust accordingly.

Reply 2

simon0

13

It is likely you ended up with:

\displaystyle \sin (2 \theta + (\pi/3)) = 1/2.

Note the range of

\theta

they are looking for:

- \pi \leq \theta \leq \pi .

Therefore the value of inverse sine must be within range:

\therefore 2(-\pi) + (\pi/3) \quad \leq \quad 2\theta +(\pi / 3) \quad \leq \quad 2(\pi) + (\pi / 3)

\, \iff \, -5 \pi / 3 \quad \leq \quad 2 \theta + ( \pi / 3) \quad \leq \quad 7 \pi / 3.

Therefore find the inverse sine values for:

\sin (2 \theta + (\pi/3)) = 1/2

in the new range above.

(edited 5 years ago)

Reply 3

apaul322

OP

11

Original post by Shaanv

Cosec(x)=1/sin(x)

Rewrite ur equation in terms of sin, rearrange and solve.

Then use ur CAST diagram or a graph to find all the solutions in the range.

Remember theta ranges from -pi to pi. But the term inside ur brackets is 2theta+pi/3 so u have to adjust accordingly.