Trig ratios for complementary angles
Trigonometric ratios of complementary angles are related by swapping sine with cosine, tangent with cotangent, and secant with cosecant.
Practice This ConceptMain explanation
Teacher explanation
Complementary angles add up to 90 degrees. In a right triangle, if one acute angle is A, the other is 90 degrees minus A. Because the two acute angles are complementary, the ratios linked to one angle become the complementary ratios of the other angle.
Example
sin(90 degrees - A) = cos A and tan(90 degrees - A) = cot A.
Simple analogy
Complementary angles swap the trig pair like a mirror.
Common confusion
Students often use the same ratio on both sides of the identity instead of switching to the complementary pair.
Exam tip
Whenever you see 90 degrees minus an angle, look for the complementary ratio, not the same one.
Study the trig ratios for complementary angles diagram carefully
Use the labelled diagram to keep trig ratios for complementary angles clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of trig ratios for complementary angles in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on trig ratios for complementary angles.
Revision cue
Revise trig ratios for complementary angles through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of trig ratios for complementary angles in one clean line.
2-mark use
Define trig ratios for complementary angles and add one example or condition.
3-mark use
Explain trig ratios for complementary angles, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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