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Can You Find... Trigonometric Edition Part 2

Age 16 to 18 Challenge Level:

This resource is from Underground Mathematics.
 

Can you find ...

(a) ... two sine graphs which only cross each other on the $x$-axis?

(b) ... a sine graph, a cosine graph and a tangent graph which all meet at certain points? What if all three graphs have to meet at the origin?

(c) ... a sine graph and a cosine graph which don't cross each other? What if the graphs have to lie between $y=1$ and $y=-1$?

(d) ... a cosine graph and a tangent graph which meet the $x$-axis the same number of times between $x=-4$ and $x=4$?  What if these points have to be the same for both graphs?


Note that by "a sine graph" we mean any curve which is obtained by some combination of stretches, reflections and translations of the graph $y=\sin x$.

This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.