11C - Exact values
Trigonometric ratios:
Some questions require knowledge of trigonometric ratios for right-angled triangles:
- SOH: \(sin(\theta)=\frac{Opposite}{Hypotenuse}\)
- CAH: \(cos(\theta)=\frac{Adjacent}{Hypotenuse}\)
- TOA: \(tan(\theta)=\frac{Opposite}{Adjacent}\)
11C - Example 1: Finding unknown side lengths using trigonometric ratios
Determine the values of \(a\) and \(b\) in the following triangle.
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11C - Example 1: Video Solution
11C - Example 1: Practice
11C - Example 1: Solutions
Question 1: \(x=18.7\;mm\) and \(y=31.1\;mm\). Question 2: \(\theta=cos^{-1}(\frac{2.1}{5.6})=68\)° |
Exact values:
11C - Example 2: Determining exact values for sine, cosine and tangent
Determine the exact values for each of the following:
(a) \(sin(\frac{5\pi}{6})\) (b) \(sin(\frac{5\pi}{3})\) (c) \(cos(\frac{7\pi}{4})\) (d) \(cos(\frac{2\pi}{3})\) (e) \(tan(\frac{7\pi}{6})\) (f) \(tan(\frac{3\pi}{4})\) |
11C - Example 2: Video solution
11C - Example 2: Practice
Question 1: State the exact value of \(sin(\frac{7\pi}{4})\). Question 2: State the exact value of \(cos(\frac{11\pi}{6})\). Question 3: State the exact value of \(tan(\frac{\pi}{3})\). 11C - Example 2: Solutions
Question 1: \(sin(\frac{7\pi}{4})=-\frac{\sqrt{2}}{2}\) Question 2: \(cos(\frac{11\pi}{6})=\frac{\sqrt{3}}{2}\) Question 3: \(tan(\frac{\pi}{3})=\sqrt{3}\) |
11C - Example 3: Determining exact values for sine, cosine and tangent
Determine the exact values for each of the following:
(a) \(sin(\frac{11\pi}{4})\) (b) \(cos(-\frac{17\pi}{6})\) (c) \(tan(-\frac{25\pi}{4})\) (d) \(tan(\frac{31\pi}{3})\) |
11C - Example 2: Video solution
11C - Example 2: Practice
Question 1: State the exact value of \(cos(\frac{9\pi}{4})\). Question 2: State the exact value of \(tan(-\frac{31\pi}{6})\). Question 3: State the exact value of \(sin(\frac{10\pi}{3})\). 11C - Example 2: Solutions
Question 1: \(cos(\frac{9\pi}{4})=\frac{\sqrt{2}}{2}\) Question 2: \(tan(-\frac{31\pi}{6})=-\frac{\sqrt{3}}{3}\) Question 3: \(sin(\frac{10\pi}{3})=-\frac{\sqrt{3}}{2}\) |