Introduction to Trigonometry and Its Applications
Introduction to Trigonometry and Its Applications tests ratios, standard angles, identities, and heights-and-distances problems. BSEB asks for exact values and for setting up a right triangle from an angle of elevation or depression.
Core rules
In a right triangle with angle θ: sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse, tanθ=opposite/adjacent; cosec, sec and cot are reciprocals.
- sin²θ+cos²θ=1; 1+tan²θ=sec²θ; 1+cot²θ=cosec²θ.
- Standard values: sin30°=1/2, cos30°=√3/2, tan45°=1, sin60°=√3/2, cos60°=1/2, tan30°=1/√3.
- Angle of elevation is measured upward from the horizontal; angle of depression is measured downward from the horizontal.
Worked example
If sinA=3/5, find cosA and tanA. Take a right triangle with opposite=3, hypotenuse=5. Adjacent=√(5²-3²)=√16=4. So cosA=4/5 and tanA=3/4.
Traps
Use the angle named; the opposite and adjacent sides swap if you change the reference angle. tan90° is undefined, and cosec0° is undefined. In height problems, draw the horizontal line at the observer’s eye level; depression is not measured from the vertical. Do not use Pythagoras with the hypotenuse as a leg.