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Wize High School Grade 12 Calculus Textbook > Derivative of Trigonometric Functions

Review of Trig Functions

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Review of Trigonometric Functions

SOH CAH TOA CAST Rule

sin⁡θ=opphypcsc⁡θ=hypoppcos⁡θ=adjhypsec⁡θ=hypadjtan⁡θ=oppadjcot⁡θ=adjopp\begin{array}{ccc} \sin\theta=\frac{opp}{hyp} & &\csc\theta=\frac{hyp}{opp}\\ \\ \cos\theta=\frac{adj}{hyp} & & \sec\theta=\frac{hyp}{adj}\\ \\ \tan\theta=\frac{opp}{adj} & &\cot\theta=\frac{adj}{opp} \end{array} • Quadrant 1: All trig ratios are positive• Quadrant 2: Only sin ratio is positive• Quadrant 3: Only tan ratio is positive• Quadrant 4: Only cos ratio is positive\begin{array}{l} •\ \text{Quadrant 1: All trig ratios are positive}\\ •\ \text{Quadrant 2: Only sin ratio is positive}\\ •\ \text{Quadrant 3: Only tan ratio is positive}\\ •\ \text{Quadrant 4: Only cos ratio is positive} \end{array}


Trig Graphs


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Special Triangles

Finding Exact Trig Values

  1. Draw out the angle given
  2. Identify the relative acute angle (RAA)--angle made with the x-axis
  3. Find the trig ratio of the RAA using special triangles
  4. Make the trig ratio positive or negative based on the CAST rule
Example: tan⁡(π3)=\tan\left(\frac{\pi}{3}\right)=

Practice: Limits of Trig Functions

Use the trig graphs to evaluate the following limits.


If the limit approaches ∞\infty or −∞-\infty, enter ∞\infty or −∞-\infty instead of DNE.