More A2 Trigonometry

5)

Find all the solutions to the equation:

cos5x + sinx = 0 for which 0° < x < 90° (or equal to..).

7)

Solve the equation sinθ - 3cos2θ = 2 , giving all the solutions between 0° and 360°.

12)

Solve the equation sin5θ - sin3θ = sinθ , giving all the solutions between 0° < θ < 180° (or equal to..).

AS CLEAR AS POSS PLEASE - REP WILL BE GIVEN IN DUE COURSE TO THOSE WHO ANSWER UNDERSTANDABLY

Reply 1

Gaz031

I'm not going to type the complete answers for you in view of both our interests - if you need a little more help feel free to reply and let me know how far you've got so far.

peperharow

5)

Find all the solutions to the equation:

cos5x + sinx = 0 for which 0° < x < 90° (or equal to..).

You can either expand cos5x into terms of sinx or write:
cos5x=-sinx
cos5x=sin(-x)
sin(90-5x)=sin(-x)
sin(90-5x)=sin(360k-x) (k is any integer)
90-5x=360k-x or 90-5x=180-(360k-x)
Rearrange both equations in terms of x, then let k take suitable integer values to give you the solutions in the required range.

7)

Solve the equation sinθ - 3cos2θ = 2 , giving all the solutions between 0° and 360°.