Study Notes Trigonometry Math 30 Pure (x,y) A r 45 1 1 2 Cosine All ...

Study Notes Trigonometry Math 30 Pure1. The primary and secondary trigonometric ratios.(x,y)sin( A)y= csc( A)=rryrAcos( A)x= sec( A)=rrxtan( A)y= cot( A)=xxy2. The CAST diagram. 3. Special triangles.2145SineAll1TangentCosine12601303

Study Notes Trigonometry Math 30 Pure4. Conversion between degreeand radian measurements.radiansdegrees=π1805. Circle formulas (using radian measure only).length of an arc of a circle = r θarea of a sector of a circle = 1 2 r2 ⋅θ6. Basic conversions : 30 º = π 6 , 45 º = π 4 , 60 º = π 3 , 90 º = π 2, 180 º = π , 360 º = 2π7. The types of trigonometric equations that are needed to be solved.a) the basic equation : 5⋅sin( x)+ 3 = 0b) "squared" equations : 4⋅cos 2 ( x) − 3 + 0c) common factor equations : 2⋅sin( x)⋅cos( x)+ sin( x)= 0d) trinomial equations that factor : 2⋅sin 2 ( x) + sin( x)− 1 = 0e) equations needing the use of identities: 2⋅sin 2 ( x) + cos( x)− 1 = 0f) equations needing technology : 4 − x 2g) multiple angle equations : 5⋅sin( 2x)− 3 = 0=2⋅cos( x)8. The parameters in the sine and cosine curves.y = a⋅sin[ b⋅( x − c)] + dandy = a⋅cos( b( x − c)) + da = amplitude =maximum − minimum2b = wave number( 2π)b= period360b= periodc = phase shiftd = displacement =maximum + minimum2

Study Notes Trigonometry Math 30 Pure9. Graphs of the basic trigonometric functions.

Study Notes Trigonometry Math 30 Pure10. Writing an equation given the graph.From the graph follow these steps:d = the displacement from the x axis to the "middle" of the given curvea = the distance of the maximum and minimum from the "middle" of the curvec = the displacement of the "start" of the curve from the y axisperiod = the "length" of the curve along the x axisb = (2 times pi) divided by the period