Exact value proofs

Prove exact values of trigonometric functions (e.g., sin 60° = √3/2) using geometric arguments.

5 questions · Easy -1.6

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OCR MEI C2 2006 January Q3
3 marks Easy -1.8
3 Fig. 3 Beginning with the triangle shown in Fig. 3, prove that \(\sin 60 ^ { \circ } = \frac { \sqrt { 3 } } { 2 }\).
OCR MEI C2 2009 June Q1
2 marks Easy -1.8
1 Use an isosceles right-angled triangle to show that \(\cos 45 ^ { \circ } = \frac { 1 } { \sqrt { 2 } }\).
OCR MEI C2 Q2
2 marks Easy -1.8
2 Use an isosceles right-angled triangle to show that \(\cos 45 ^ { \circ } = \frac { 1 } { \sqrt { 2 } }\).
OCR MEI C2 Q7
3 marks Moderate -0.8
7 You are given that \(\tan \theta = \frac { 1 } { 2 }\) and the angle \(\theta\) is acute. Show, without using a calculator, that \(\cos ^ { 2 } \theta = \frac { 4 } { 5 }\).
OCR MEI C2 Q9
3 marks Easy -1.8
9 Fig. 3 Beginning with the triangle shown in Fig. 3, prove that \(\sin 60 ^ { \circ } = \frac { \sqrt { 3 } } { 2 }\).