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sinB y secA en triángulo rectángulo

Question about use of trig identities, student has to use identities to find exact value of \(\sin \frac{\pi}{12}\). Question is used in exam where student has to write out the solution and upload it for grading.

Question about use of trig identities, student has to use identities to find exact value of \(\cos \frac{7\pi}{12}\). Question is used in exam where student has to write out the solution and upload it for grading.

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V $ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time. 

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Use Pythagoras' Theorem to find the length of a side on a right-angled triangle.

DCS 2023 Maths Entrance Test to be used September 2023

1.5 hours with 3 randomised questions from each of these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry

More difficult trigonometric equations with radians

Solving $\cos(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

More work on differentiation with trigonometric functions

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Choose one from a list to identify the function shown in a graph. The function is a randomly selected sin, cos, or tan graph with random scale factor.

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A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use SOH CAH TOA to find the side indicated with an x.

Calculating the missing side-length of a triangle using the cosine rule.

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

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several statements are given regarding trig identities. student is to select which are true and which are false

Students are shown a right angled triangle and asked to find the value of an angle using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is to be given in degrees and minutes.

There are 4 orientations of the triangle in the diagram. The orientation is randomly chosen.

Students are shown a right angled triangle and asked to compute a side length using a trig identity.

The triangle is a fixed image, but the angles and side lengths are randomly selected.

The angle is given in degrees and minutes, and students are asked for the side length correct to 1 decimal place.

There are 4 different triangle orientations that can display.

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Solve a trigonometric equation

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

JPO 126 Class test 7