IB Math SL Trigonometry

Here you will find original IB Math SL exam style trigonometry practice problems. Visit this page directly at hunkim.com/sltrigonometry

1. Solve \ln(2\sin x)+\ln(\cos x)=0, \pi \leq x \leq 3\pi
2. f(x)=\sin(2x) and g(x)=4x^2-2
   1. Find f\left( \frac{\pi}{2} \right)
   2. Find \left(g\circ f\right)\left(\frac{\pi}{2}\right)
3. f(x)=\sqrt{3}e^{3\theta}\sin \theta+e^{3\theta}\cos \theta, 0\leq \theta \leq 2\pi. Solve f(x)=0.
4. Let h=\sin 50^\circ and k=\cos 100^\circ. Give your answers to the following in terms of h and k.
   1. Write down an expression for
      1. \sin 130^\circ
      2. \cos 80^\circ
   2. Find an expression for \cos 130^\circ
   3. Find an expression for \tan 130^\circ
5. The expression 8\sin \alpha \cos \alpha can be expressed in the form p \sin(qx).
   1. Find the value of p and q.
   2. Hence or otherwise, solve the equation 8\sin\alpha \cos\alpha=-2, for -\frac{\pi}{6}\leq \alpha \leq \frac{2\pi}{3}

Answers

1. \frac{5\pi}{4}, \frac{9\pi}{4}
2. 1. 0
   2. -2
3. \frac{5\pi}{6} and \frac{11\pi}{6}
4. 1. 1. h
      2. -k
   2. -\sqrt{1-h^2}
   3. \frac{h}{\sqrt{1-h^2}}
5. 1. p=4 and q=2
   2. -\frac{\pi}{12}, \frac{7\pi}{12}