Find exact trig values from given ratio

A question is this type if and only if you are given one trigonometric ratio (like sin θ or cos θ) and must find the exact value of another ratio (like tan θ) without a calculator.

8 questions · Moderate -0.7

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CAIE P1 2022 November Q6
5 marks Moderate -0.3
6 It is given that \(\alpha = \cos ^ { - 1 } \left( \frac { 8 } { 17 } \right)\).
Find, without using the trigonometric functions on your calculator, the exact value of \(\frac { 1 } { \sin \alpha } + \frac { 1 } { \tan \alpha }\).
OCR MEI C2 2007 January Q3
3 marks Moderate -0.8
3 Given that \(\cos \theta = \frac { 1 } { 3 }\) and \(\theta\) is acute, find the exact value of \(\tan \theta\).
OCR MEI C2 Q3
4 marks Moderate -0.8
3 Given that \(A\) is the obtuse angle such that \(\sin A = \frac { 1 } { 5 }\), find the exact value of \(\cos A\).
OCR MEI C2 Q5
3 marks Moderate -0.8
5 You are given that \(\sin \theta = \frac { \sqrt { 2 } } { 3 }\) and that \(\theta\) is an acute angle. Find the exact value of \(\tan \theta\).
OCR MEI C2 Q8
3 marks Moderate -0.8
8 Given that \(\cos \theta = \frac { 1 } { 3 }\) and \(\theta\) is acute, find the exact value of \(\tan \theta\).
OCR MEI C2 2010 January Q3
3 marks Moderate -0.8
3 You are given that \(\sin \theta = \frac { \sqrt { 2 } } { 3 }\) and that \(\theta\) is an acute angle. Find the exact value of \(\tan \theta\).
AQA AS Paper 2 2019 June Q3
2 marks Moderate -0.8
3 It is given that \(\sin \theta = - 0.1\) and \(180 ^ { \circ } < \theta < 270 ^ { \circ }\) Find the exact value of \(\cos \theta\)
AQA Paper 1 2023 June Q10
8 marks Moderate -0.3
10
  1. Point \(A\) on the curve has coordinates ( \(a , 0.5\) )
    10
    1. Find the value of \(a\)
      10
  3. (ii) State the value of \(\sin \left( 180 ^ { \circ } - a ^ { \circ } \right)\)
    10
  4. Point \(B\) on the curve has coordinates \(\left( b , - \frac { 3 } { 7 } \right)\)
    10
    1. Find the exact value of \(\sin \left( b ^ { \circ } - 180 ^ { \circ } \right)\)
      10
  6. (ii) Find the exact value of \(\cos b ^ { \circ }\)