Trigonometry
Trigonometry in Bagrut covers the unit circle, identities, trigonometric equations, and triangle solving with the sine and cosine rules. Questions often combine an identity with a restricted interval, or a geometric diagram with a bearing or area calculation.
Core rules
- sin²θ+cos²θ=1 and tanθ=sinθ/cosθ, with cosθ≠0.
- On the unit circle, cosθ is the x-coordinate and sinθ the y-coordinate; signs depend on the quadrant.
- General solution: if sinθ=s, then θ=arcsin s+2πk or θ=π−arcsin s+2πk.
- Sine rule: a/sinA=b/sinB=c/sinC=2R, where R is the circumradius.
- Cosine rule: a²=b²+c²−2bc cosA.
- Area of a triangle: ½ab sinC.
Worked example
Solve 2sin²x−sinx−1=0 for 0≤x<2π. Let t=sinx. Then 2t²−t−1=0, so (2t+1)(t−1)=0, giving t=1 or t=−½. sinx=1 gives x=π/2. sinx=−½ gives x=7π/6 and x=11π/6. All four solutions lie in the interval. The substitution is valid because it is only a renaming of sinx, and each t-value is checked against the range of sine.
Traps
Dividing by sinx can lose the solution sinx=0. Calculator mode must match radians or degrees. In the ambiguous SSA case, the sine rule may give two possible angles; check whether both fit the triangle. Do not use the cosine rule with an angle opposite the wrong side.