5.6 Chapter Review
5.6.1 Chapter summary
Degree and radian measures describe the same rotations. Right-triangle ratios, reference angles, and the unit circle extend trigonometry to all angles. Sine and cosine model periodic behaviour through amplitude, period, phase shift, and midline. Inverse functions recover principal angles, while identities and angle formulas support exact rewriting and verification.
5.6.2 Common mistakes
- Using the wrong calculator angle mode.
- Assigning the wrong sign after finding a reference angle.
- Confusing inverse trigonometric functions with reciprocals.
- Reporting only the principal value when an interval requires multiple angles.
- Applying a horizontal transformation in the wrong direction.
5.6.3 Exercises
- Convert \(11\pi/9\) to degrees.
Check Your Work
\(220^\circ\). - Find all six ratios for a 5-12-13 triangle.
Check Your Work
Relative to the angle opposite 5: \(\sin=5/13\), \(\cos=12/13\), \(\tan=5/12\) and reciprocals. - Evaluate \(\sin(5\pi/4)\).
Check Your Work
\(-\sqrt2/2\). - Analyze \(y=-3\cos(2x)+4\).
Check Your Work
Amplitude 3, period \(\pi\), midline 4, reflected. - Solve \(\cos\theta=-0.6\) for one revolution.
Check Your Work
\(\theta\approx126.9^\circ,233.1^\circ\). - Verify \((1-\cos^2x)/\sin x=\sin x\) where defined.
Check Your Work
\(1-\cos^2x=\sin^2x\), then divide by \(\sin x\).