Tangents Worked Solution – 2020 NCEA Level 3 Q1(b) (AS91578)

Question

Scanned exam prompt asking for the tangent gradient of a trigonometric function at a specified point.

First walkthrough idea

Focus to try first

Trig derivatives and evaluating a tangent gradient.

Step 1

Differentiate the trigonometric terms

Differentiate the function using trig derivatives and the chain rule.

Show the first step’s working

y=3\sin(2x)+\cos(2x) \] \[ \frac{dy}{dx} = 3\cos(2x)\cdot 2-\sin(2x)\cdot 2 \] \[ \frac{dy}{dx}=6\cos(2x)-2\sin(2x)

Walkthrough overview

What this question practises

This 2020 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Trig derivatives and evaluating a tangent gradient.

This is Question 1(b) from the 2020 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

Page updated 9 August 2026.

Learning summary

Review the method, not only the answer

This walkthrough helps you practise trig derivatives and evaluating a tangent gradient. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Use the derivative for the gradient and the original curve for the point before forming the tangent equation.

Continue practising

← Question 1(a) Question 1(c) →