2 interactive labs · AS & A Level Mathematics 9709
Sine, Cosine and Tangent Graphs
1.5 Trigonometry · Change a, b, c and d in y = a sin(bx + c) + d, in degrees or radians, then read the period, range and asymptotes and solve y = k in an interval.
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About this lab
Change a, b, c and d in y = a sin(bx + c) + d, in degrees or radians, then read the period, range and asymptotes and solve y = k in an interval.
You will be able to
Describe how a, b, c and d change the graph of y = a sin(bx + c) + d, and the cosine and tangent forms, including the period, range and asymptotes.
State the exact values of sin, cos and tan of 30°, 45°, 60° and their related angles, and use them to give the coordinates of points on a graph.
Determine the number and values of the solutions of y = k in a stated interval, in degrees or radians, from the intersections of the line and the graph.
Trig Equations in a Stated Interval
1.5 Trigonometry · Solve sin, cos and tan equations from the reference angle, test every candidate against the stated interval and reject the rest with a reason.
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About this lab
Solve sin, cos and tan equations from the reference angle, test every candidate against the stated interval and reject the rest with a reason.
You will be able to
Determine all the solutions of a simple trigonometric equation in a stated interval, using the reference angle, the quadrant rule and whole turns.
Explain why an equation in sin bx is solved for bx over the interval multiplied by b, and why the values found are then divided by b.
Reduce an equation to one trigonometric function using tan θ ≡ sin θ ÷ cos θ and sin²θ + cos²θ ≡ 1, and reject a value of sin or cos outside −1 to 1 with its reason.
State each solution exactly when it is exact, otherwise to 1 d.p. in degrees or 3 s.f. in radians, excluding the end points of a strict interval.
