Sketching & Analyzing Trig Graphs (sec/csc/cot & roots)

SAT Score Range

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1 session

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This series ended on December 4, 2025. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

In this one-session class we will use A-level style questions to practise sketching reciprocal trig graphs and using them to analyse equations. We’ll sketch graphs of sec x, csc x, and cot x, then draw suitable pairs of graphs to show that certain trig equations have one root or exactly two roots in a given interval. We will finish by proving and using a trig identity to sketch a more challenging graph. Expect lots of sketching, discussion of asymptotes and key points, and careful reasoning about how many solutions exist.
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Tutored by

Tasheen U 🇧🇩

Certified in 17 topics

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A recent graduate of CAIE A-levels with Mathematics, Physics, and Computer Science. Currently, pursuing my B.Sc. in Computer Science & Engineering. Passionate about math and education, I am eager to help others excel in subjects including math, physics, computer science, and SAT Prep. Excited to tutor in various math areas such as Algebra, Geometry, Pre-Calculus, Calculus, and Statistics. Let's learn and grow together!

Sessions

✋ ATTENDANCE POLICY

Please join on time and plan to stay for the full 60 minutes. This is a problem-solving session, so I expect everyone to participate: trying sketches on paper, sharing ideas in the chat, and explaining reasoning. If you know in advance that you cannot attend or will be more than 5 minutes late, please unregister so another learner can take the spot.

SESSION 1

4

Dec

SESSION 1

Trigonometry

Thu 4:00 AM - 5:00 AM UTCDec 4, 4:00 AM - 5:00 AM UTC

We will work through a focused set of A-level style graph questions involving trigonometric functions:
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• Sketch the graph of y = sec x over one full cycle.  
• Use pairs of graphs (e.g., y = csc x with a straight line or quadratic) to show that equations like csc x = (1/2)x + 1, 2 cot x = 1 + e^x, sec x = 3 − (1/2)x^2, and csc x = x(π − x) have exactly one or two roots in a given interval.  
• Prove a trig identity involving tan(45° ± x) and use it to sketch the resulting graph of y = tan(45° + x) + tan(45° − x).
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Throughout, we’ll emphasise:
– how to choose a “suitable pair of graphs”,  
– how to mark key points and asymptotes,  
– and how to argue clearly about the number of intersections (roots).
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Please bring graph paper, pen, and a calculator; a ruler is helpful but not required.
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Public Discussion

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Dec 4

1 week

60 mins

/ session

SCHEDULE

Thursday, Dec 4

4:00AM