(a) State the complementary angle relationship between the sine and cosine of two…
MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
(a) State the complementary angle relationship between the sine and cosine of two acute angles in a right-angled triangle.
(a) State the complementary angle relationship between the sine and cosine of two acute angles in a right-angled triangle.
(b) For an acute angle θ, it is given that sinθ=cosθ. Using only fundamental trigonometric identities, prove that θ=45∘.
(c) Give a right-triangle explanation (with appropriate reasoning, but without a diagram) to justify why the value obtained in part (b) is unique for 0∘<θ<90∘.