Trigonometric Functions and addition formula

• What unit of angular measurement is used in trigonometric equations?

  Radians
• What is the value of $0^\circ$ in radians?


  0
• What is the value of $30^\circ$ in radians?


  $\pi/6$
• What is the value of $45^\circ$ in radians?


  $\pi/4$
• What is the value of $60^\circ$ in radians?


  $\pi/3$
• What is the value of $90^\circ$ in radians?


  $\pi/2$
• What unit of angular measurement is commonly used in trigonometric equations?

  Degrees
• What is the value of $0^\circ$ in degrees?


  $0°$
• What is the value of $30^\circ$ in degrees?


  $30°$
• What is the value of $45^\circ$ in degrees?


  $45°$
• What is the value of $60^\circ$ in degrees?


  $60°$
• What is the value of $90^\circ$ in degrees?


  $90°$
• What trigonometric function is represented by $\sin?$


  Sine
• What is the value of $\sin 0^\circ?$


  0
• What is the value of $\sin 30^\circ?$


  $1/2$
• What is the value of $\sin 45^\circ?$


  $1/\sqrt{2}$
• What is the value of $\sin 60^\circ?$


  $\sqrt{3}/2$
• What is the value of $\sin 90^\circ?$


  1
• What trigonometric function is represented by $\cos?$


  Cosine
• What is the value of $\cos 0^\circ?$


  1
• What is the value of $\cos 30^\circ?$


  $\sqrt{3}/2$
• What is the value of $\cos 45^\circ?$


  $1/\sqrt{2}$
• What is the value of $\cos 60^\circ?$


  $1/2$
• What is the value of $\cos 90^\circ?$


  0
• What trigonometric function is represented by $\tan?$


  Tangent
• What is the value of $\tan 0^\circ?$


  0
• What is the value of $\tan 30^\circ?$


  $1/\sqrt{3}$
• What is the value of $\tan 45^\circ?$


  1
• What is the value of $\tan 60^\circ?$


  $\sqrt{3}$
• What is the value of $\tan 90^\circ?$


  ∞
• In functions of the form $y =$$a \sin(bx + c)$ and $y =$$a \cos(bx + c),$ what does $a$ represent?


  • Amplitude (positive value of $a)$
• In trigonometric functions of the form $y =$$a \sin(bx + c)$ and $y =$$a \cos(bx + c),$ what is the period of the graph?


  • Length of one full wave
• For sine and cosine graphs, how is the period derived in terms of $b?$


  • Divide $360^\circ$ by $b$
• What is the effect of the value of $c$ in trigonometric functions of the form $y =$$a \sin(bx + c)$ and $y =$$a \cos(bx + c)?$


  It translates the graph vertically.
• In trigonometric functions of the form $y =$$a \sin(x + b)$ and $y =$$a \cos(x + b),$ what does $a$ represent and what is the effect of $b?$


  • $a$ represents the amplitude.
  • The value of $b$ translates the graph horizontally.
• What two methods can be used to solve trigonometric equations according to the National 5 checklist?

  • CAST diagram method
  • Graphical method
• Why is it important to know exact values in trigonometry?

  • To solve trigonometric equations efficiently and accurately
• What are exact values in trigonometry?

  Specific values of trigonometric functions for standard angles such as $30^\circ,$ $45^\circ,$ and $60^\circ$
• Besides $30^\circ,$ $45^\circ,$ and $60^\circ,$ which angles should you know the exact values of sine and cosine for?


  • $90^\circ,$ $180^\circ,$ $270^\circ,$ $360^\circ$
• How can exact values be used in solving trigonometric equations?

  They allow you to solve equations without using a calculator, focusing on trigonometric relationships.