Simplify or verify trig identity with acute angle

Questions that give a specific trig value (e.g. tan θ = 1/2) with an acute angle constraint and ask to show or verify a result (e.g. cos²θ = 4/5), or simplify a trig expression, without requiring quadrant sign analysis.

4 questions · Moderate -0.9

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1
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CAIE P1 2013 November Q1
3 marks Easy -1.2
1 Given that \(\cos x = p\), where \(x\) is an acute angle in degrees, find, in terms of \(p\),
  1. \(\sin x\),
  2. \(\tan x\),
  3. \(\tan \left( 90 ^ { \circ } - x \right)\).
OCR MEI C2 2008 January Q3
3 marks Moderate -0.8
3 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 Q3
3 marks Moderate -0.8
3 Simplify \(\frac { \sqrt { 1 - \cos ^ { 2 } \theta } } { \tan \theta }\), where \(\theta\) is an acute angle.
[0pt] [3]
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 \(\cos ^ { 2 } \theta = \frac { 4 } { 5 }\).