Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometry - auxilliary angles.
Test Yourself 1 - solutions.


 

1. 2. .
3. (i)

(ii)

4.
5.

6. (i)

(ii) Hence sketch y = sin x + cos x (for -π ≤ x ≤ 2π)?

(iii) How many solutions are there for sin x + cos x = 1 within that domain?

As = 1 at x = 2π (due to the horizontal shift), there are three solutions to the equation.
7. 8. (i)

(ii) Sketch the curve for 0° ≤ x ≤ 360° .
9. (i)
(ii) Hence or otherwise solve
for 0 ≤ β ≤ 2π.

10. (i)

(ii)

11.

 

 12.
13. 14.
15. 16. (i)

(ii)

17. (i)

(ii) Initial height is 12 metres (= 13sin (1.176)).

(iii)

18. (i)

(ii)

(iii)

19. (i)

(ii)

20.