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Exact-Trig-Values Aqa Foundation

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Exam code:8300

Exact trig values

What are exact values in trigonometry?

For certain angles the values of sin θ, cos θ and tan θ can be written exactly
- This means using fractions and surds
You are expected to know the exact values of sin, cos and tan for
- 0°, 30°, 45°, 60°, 90°, 180° and their multiples

$theta$	0º	30º	45º	60º	90º
sin $theta$	0	$1 half$	$fraction numerator square root of 2 over denominator 2 end fraction$	$fraction numerator square root of 3 over denominator 2 end fraction$	1
cos $theta$	1	$fraction numerator square root of 3 over denominator 2 end fraction$	$fraction numerator square root of 2 over denominator 2 end fraction$	$1 half$	0
tan <img alt=”theta” data-mathml=”<math ><semantics><mi>θ</mi><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2211%22%20wrs%3Abaseline%3D%2216%22

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