Unit 4 · Core unit
Extending trigonometry beyond right triangles. Structure and symmetry replace memorisation, which is what makes unfamiliar angles tractable.
What a strong answer looks like
A strong answer settles the quadrant before the value, because sign errors outnumber every other kind here.
Know
A radian is the angle whose arc equals the radius, so arc length is the radius times the angle and sector area is half the radius squared times the angle.
Apply
Convert to radians before applying either formula.
Watch out
Applying a radian formula to an angle still measured in degrees.
Study move
Compute arc length and sector area for a circle of known radius.
Know
The coordinates of the terminal point are the cosine and sine of the angle, and symmetry generates every quadrant from the first.
Apply
Find the reference angle, take the magnitude from a special triangle, then attach the quadrant sign.
Watch out
Producing the right magnitude with the wrong sign.
Study move
State quadrant, reference angle, and signs for four angles before evaluating.
Know
Tangent, cotangent, secant, and cosecant are all quotients or reciprocals of sine and cosine.
Apply
Reduce any of the six to sine and cosine, then evaluate.
Watch out
Inverting the ratio when computing tangent from sine and cosine.
Study move
Given a sine value and a quadrant, produce all six function values.
Modeling drill
A circle of radius 6 has a central angle of 2 radians. Find the arc length and sector area, then convert the angle to degrees.
